main_SN_others.cpp

#include <iostream>
#include <fstream>
#include <iomanip>   // format manipulation
#include <string>
#include <sstream>
#include <cstdlib>
#include <math.h>
#include <cmath>
#include <gsl/gsl_math.h>
#include <gsl/gsl_linalg.h>
#include <stdio.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_test.h>
#include <gsl/gsl_multimin.h>
#include <vector> // C++ vector class
#include <algorithm>
#include <functional>
#include <gsl/gsl_randist.h>
#include <boost/numeric/conversion/cast.hpp>
#include <boost/lexical_cast.hpp>
#include <gsl/gsl_rng.h>
#include <unistd.h>
#include <filein.h>
//#include <csvreader.h>
#include <limits>
#include <float.h>
#include <time.h>
#include <sys/time.h>
#include <chrono>
//#include <windows.h>
#include <omp.h>
#include <matrix_ops2.h>
#include <dist_corr.h>
#include <kernel.h>
#include <power.h>
//#include <tests.h>
#include <dgp.h>
#include <nl_dgp.h>
#include <nongaussian_reg.h>
#include <dep_tests.h>
#include <nongaussian_dist_corr.h>
#include <nongaussian_power.h>


using namespace std;

//void (*aktfgv)(double *,double *,int *,int *,void *,Matrix&);

int main(void) {

	//start the timer%%%%%
    //time = ((double) clock())/((double) CLOCKS_PER_SEC);
    auto time = std::chrono::high_resolution_clock::now();
    auto timelast = time;

    #if 0 //begin comment
    /*auto T = 100, N = 1000, TL = 2, lag_smooth = 5;
    Matrix X(T,1), Y1(T,1), Y2(T,1), resid(T-2,1), slope(6,1), alpha_X(6,1), alpha_Y(6,2), delta(3,1);
    alpha_X(1) = 0.01;
    alpha_X(2) = 0.2;
    alpha_X(3) = 0.03;
    alpha_X(4) = -0.6;
    alpha_X(5) = -0.1;
    alpha_X(6) = 0.1;
    alpha_Y(1,1) = 0.04;
    alpha_Y(2,1) = 0.2;
    alpha_Y(3,1) = 0.04;
    alpha_Y(4,1) = -0.7;
    alpha_Y(5,1) = 0.1;
    alpha_Y(6,1) = 0.1;
    alpha_Y(1,2) = 0.05;
    alpha_Y(2,2) = 0.8;
    alpha_Y(3,2) = -0.05;
    alpha_Y(4,2) = -0.5;
    alpha_Y(5,2) = -0.1;
    alpha_Y(6,2) = 0.1;
    delta(1) = 0.1;
	delta(2) = 0.2;
	delta(3) = -0.1;
	gsl_rng *r = nullptr;
    const gsl_rng_type *gen; //random number generator
    gsl_rng_env_setup();
    gen = gsl_rng_taus;
    r = gsl_rng_alloc(gen);
    gsl_rng_set(r, 525323);
    unsigned long rseed = 1;
    for (int i = 1; i <= 100; ++i) {
          rseed = gsl_rng_get (r);
          NL_Dgp::gen_Bilinear <NL_Dgp::gen_TriSN> (X, Y1, Y2, alpha_X, alpha_Y, delta, -0.7, 0.5, 0, rseed);
          NL_Dgp::est_BL (resid, slope, Y2);
          cout << resid(1) << endl;
     }
     gsl_rng_free (r);
    double rho12 = 0.4, rho13 = -0.4, res_X = 0., res_Y = 0.;*/
	/*Matrix lag_t1(3,1), lag_t2(3,1), xy_t(3,1), xy_s(3,1), lag_s1(3,1), lag_s2(3,1), delta(3,1);
	lag_t1(1) = 0.85;
	lag_t1(2) = 0.7;
	lag_t1(3) = -0.6;
	lag_t2(1) = -0.5;
	lag_t2(2) = 0.53;
	lag_t2(3) = 0.8;
	lag_s1(1) = -0.85;
	lag_s1(2) = 0.5;
	lag_s1(3) = -0.8;
	lag_s2(1) = 0.23;
	lag_s2(2) = -0.95;
	lag_s2(3) = 0.8;
	xy_t(1) = 0.1;
	xy_t(2) = 0.8;
	xy_t(3) = -0.7;
	xy_s(1) = -0.5;
	xy_s(2) = 0.6;
	xy_s(3) = 1.5;
	delta(1) = 0.7;
	delta(2) = 0.5;
	delta(3) = -0.6;*/
     /*Matrix REJF_Hong(2,1), REJF_ECFTest(2,1), REJF_Haugh(2,1), cv_Hong(2,1), cv_ECFTest(2,1), cv_Haugh(2,1), asymp_CV_Hong(2,1), asymp_CV_Haugh(2,1);
    asymp_CV_Hong(1) = 1.645;//5%-critical value from the standard normal distribution
    asymp_CV_Hong(2) = 1.28;//10%-critical value from the standard normal distribution
    auto number_sampl = 500, bandW = 5, choose_alt = 2;
    asymp_CV_Haugh = Dep_tests::asymp_CV_ChiSq (bandW);
    double delta = 0.1;
    ofstream size_out;
    string size_out_filename = "./temp/size.txt";
	size_out.open (size_out_filename.c_str(), ios::out);
    Dep_tests::cValue <bartlett_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (REJF_Hong, REJF_ECFTest, REJF_Haugh, cv_Hong, cv_ECFTest,
                                                                                               cv_Haugh, alpha_X, alpha_Y, asymp_CV_Hong, asymp_CV_Haugh, number_sampl, T, bandW, delta, 13432552, size_out);
    size_out.close();*/
    /*Matrix empir_REJF_Hong(2,1), asymp_REJF_Hong(2,1), empir_REJF_ECFTest(2,1), asymp_REJF_ECFTest(2,1), empir_REJF_Haugh(2,1), asymp_REJF_Haugh(2,1);
    ofstream pwr_out;
    string pwr_out_filename = "./temp/power.txt";
    pwr_out.open (pwr_out_filename.c_str(), ios::out);
    Dep_tests::power_f<bartlett_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest, empir_REJF_Haugh,
                                                  asymp_REJF_Haugh, alpha_X, alpha_Y, cv_Hong, asymp_CV_Hong, cv_ECFTest, asymp_CV_Hong, cv_Haugh, asymp_CV_Haugh, number_sampl, T, bandW,
                                                  delta, 0.8, choose_alt, 5325325325, pwr_out);
    pwr_out.close();*/
    //NGReg::breg <NL_Dgp::gen_TriSN, NGReg::cmean_TAR> (&res_X, &res_Y, lag_t1, lag_t2, lag_s1, lag_s2, alpha_X, alpha_Y, delta, rho12, rho13, 1.5, r, 1325325);
    //NGReg::var_U_ts <NL_Dgp::gen_SN, NGReg::cmean_TAR> (&res_X, &res_Y, xy_t, xy_s, lag_t1, lag_t2, lag_s1, lag_s2, alpha_X, alpha_Y,0.7, -0.5, 1.5, r, 1342525);
    //NGReg::var_U_ts <NL_Dgp::gen_SN, NGReg::cmean_BL> (res_X, res_Y, xy_t, xy_s, lag_t1, lag_t2, lag_s1, lag_s2, alpha_X, alpha_Y, delta(1), 1.5, 1352543564);
	//cout << res_X << " , " << res_Y << endl;
	//generate data
	/*unsigned long seed = 6436;
	Matrix data_X(T,1), data_Y1(T,1), data_Y2(T,1), epsilon_t(N,1), eta1_t(N,1), eta2_t(N,1), epsilon_s(N,1), eta1_s(N,1), eta2_s(N,1);
    NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN> (data_X, data_Y1, data_Y2, alpha_X, alpha_Y, delta, rho12, rho13, 1, seed);
    NL_Dgp::gen_RANV<NL_Dgp::gen_TriSN> (epsilon_t, eta1_t, eta2_t, delta, 0., 0., 0, 13435);
    NL_Dgp::gen_RANV<NL_Dgp::gen_TriSN> (epsilon_s, eta1_s, eta2_s, delta, 0., 0., 0, 53435);
    cout << epsilon_t(1) << " , " << epsilon_s(1) << " , " << eta1_t(1) << " , " << eta1_s(1) << " , " << eta2_t(1) << " , " << eta2_s(1) << endl;
    auto kernel_QDSum = 0., kernel_QRSum = 0.;
    NGDist_corr::integrate_Kernel <daniell_kernel> (kernel_QDSum, kernel_QRSum);
	cout << NGDist_corr::do_Test<daniell_kernel, NGReg::cmean_BL> (data_X, data_Y1, data_Y2, TL, lag_smooth, kernel_QRSum, alpha_X, alpha_Y, epsilon_t,
	                                                               epsilon_s, eta1_t, eta1_s, eta2_t, eta2_s, 1.5) << endl;*/



	/*Matrix asymp_REJF(2,1), empir_CV(2,1), asymp_CV(2,1), epsilon_t(N,1), epsilon_s(N,1), eta_t(N,1), eta_s(N,1);
	auto number_sampl = 500;
	auto expn = 1.5;
	asymp_CV(1) = 1.645;//5%-critical value from the standard normal distribution
    asymp_CV(2) = 1.28;//10%-critical value from the standard normal distribution
    ofstream size_out;
    string size_out_filename = "./temp/size.txt";
	size_out.open (size_out_filename.c_str(), ios::out);
	NL_Dgp::gen_RANV<NL_Dgp::gen_SN> (epsilon_t, eta_t, delta(1), 0., 0, 13435); //generate random errors
    NL_Dgp::gen_RANV<NL_Dgp::gen_SN> (epsilon_s, eta_s, delta(1), 0., 0, 53435);
    NGPower::cValue<bartlett_kernel,NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>,NGReg::cmean_BL, NL_Dgp::est_BL> (asymp_REJF, empir_CV, number_sampl, T, TL, lag_smooth,
                                                                                                           alpha_X, alpha_Y, epsilon_t, epsilon_s, eta_t, eta_s,
																										   delta(1), expn, asymp_CV, 1234235, size_out);
    size_out.close();*/
    auto T = 200, number_sampl = 500, bandW = 5;
    Matrix X(T, 1), Y1(T, 1), Y2(T, 1), alpha_X(6, 1), alpha_Y(6, 2), delta(3,1);
    alpha_X(1) = 0.01;
    alpha_X(2) = 0.2;
    alpha_X(3) = 0.03;
    alpha_X(4) = -0.6;
    alpha_X(5) = -0.1;
    alpha_X(6) = 0.1;
    alpha_Y(1,1) = 0.04;
    alpha_Y(2,1) = 0.2;
    alpha_Y(3,1) = 0.04;
    alpha_Y(4,1) = -0.7;
    alpha_Y(5,1) =  0.1;
    alpha_Y(6,1) = 0.1;
    alpha_Y(1,2) = 0.05;
    alpha_Y(2,2) = 0.8;
    alpha_Y(3,2) = -0.05;
    alpha_Y(4,2) = -0.5;
    alpha_Y(5,2) = -0.1;
    alpha_Y(6,2) = 0.1;
    delta(1) = 0.1;
    delta(2) = 0.1;
    delta(3) = -0.1;
    double rho12 = -0.2056, rho13 = 0.2671;
	int choose_alt = 2;
	unsigned long seed = 24532523;
	Matrix REJF_ElHimdiRoy(2,1), empir_CV_ElHimdiRoy(2,1), empir_REJF_ElHimdiRoy(2,1), asymp_REJF_ElHimdiRoy(2,1);
	Matrix asymp_CV_ElHimdiRoy = Dep_tests::asymp_CV_ChiSq2 (bandW);//obtain 5%- and 10%- asymptotic critical values for the test
    //NL_Dgp::gen_TAR<NL_Dgp::gen_TriSN>(X, Y1, Y2, alpha_X, alpha_Y, delta, rho12, rho13, choose_alt, 1242432);
    //NL_Dgp::gen_TAR<NL_Dgp::gen_SN>(X, Y, alpha_X, alpha_Y, delta(1), rho12, choose_alt, 12424);
    //NL_Dgp::est_TAR (resid, slope, Y);
     ofstream size_out;
	size_out.open ("./temp/size.txt", ios::out);
     Dep_tests::cValue <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (REJF_ElHimdiRoy, empir_CV_ElHimdiRoy, alpha_X, alpha_Y,
                                                                       delta, asymp_CV_ElHimdiRoy, number_sampl, T, bandW, seed, size_out);
    size_out.close();
    cout << "5% and 10% sizes are " << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << endl;
    ofstream pwr_out;
	pwr_out.open ("./temp/power.txt", ios::out);
    Dep_tests::power_f <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, -0.5, 0.2, choose_alt, number_sampl, T, bandW, seed, pwr_out);
     pwr_out.close();
    #endif //end comment

    #if 0 //begin comment
    /***********************************************************************************************************************************************************/
    /*********************************************************** Start Calculating the Proposed Test Using Real Data *******************************************/
	//Import a csv file of oil prices
    ifstream oildata;
    oildata.open ("./Application/oilprices_1977-1978.csv", ios::in);
    if (!oildata)
        return(EXIT_FAILURE);
    vector<string> oildata1;
    loadCSV(oildata, oildata1);
    int T = oildata1.size() - 1; //Rows
    Matrix X(T, 1);
    for (auto i = 1; i <= T; i++)
        X(i) = (hex2d(oildata1[i]) - hex2d (oildata1[i-1])) / hex2d (oildata1[i-1]);//calculate oil returns
    oildata.close();
    //Import a csv file of stock prices
    ifstream stockdata;
    stockdata.open ("./Application/stockprices_1977-1978.csv", ios::in);
    if (!stockdata)
        return(EXIT_FAILURE);
    vector<vector<string>* > stockdata1;
    loadCSV(stockdata, stockdata1);
    int nC = (*stockdata1[1]).size(); //Columns
    Matrix Y(T, nC);
    for (auto i = 1; i <= T; ++i)
    {
        for (auto j = 1; j <= nC; ++j)
        {
            Y(i,j) = (hex2d ((*stockdata1[i])[j-1]) - hex2d ((*stockdata1[i-1])[j-1])) / hex2d ((*stockdata1[i-1])[j-1]);//calculate stock returns
        }
    }
    for (vector<vector<string>*>::iterator p = stockdata1.begin( ); p != stockdata1.end( ); ++p)
    {
        delete *p;
    }
    stockdata.close();
    //Write returns to file
    ofstream returns;
    string returns_filename = "./Application/returns_1977-1978.csv";
	returns.open (returns_filename.c_str(), ios::out);
	returns << "S&P 500" << " , " << "NYSE Composite" << " , " << "NASDAQ" << " , " << "OK WTI Oil" << endl;
	for (auto i = 1; i <= T; ++i)
    {
        for (auto j = 1; j <= nC; ++j)
        {
            returns << Y(i,j) << " , ";
        }
        returns << X(i) << "\n";
    }
	returns.close();
    /*ofstream returns;
    string returns_filename = "./Application/returns.csv";
	returns.open (returns_filename.c_str(), ios::out);
	returns << "S&P 500" << " , " << "NYSE Composite" << " , " << "NASDAQ" << " , " << "OK WTI Oil Spot Price" << endl;
	for (auto i = 1; i <= T; ++i)
    {
        for (auto j = 1; j <= nC; ++j)
        {
            returns << Y(i,j) << " , ";
        }
        returns << X(i) << "\n";
    }
	returns.close();*/

    int lag_len = 20; //AR lag length
    int lag_smooth = 20; //a bandwidth for the proposed statistic
    Dgp dgp_obj;
    Matrix resid_X(T-lag_len, 1), slope_X(lag_len+1, 1), Yj(T, 1), resid_Yj(T-lag_len, 1), slope_Yj(lag_len+1, 1), resid_Y(T-lag_len, nC);
    double SSR = 0.;
    dgp_obj.est_AR (resid_X, slope_X, SSR, X, lag_len);//fit X to an AR(lag_len) process, and obtain a sequence of residuals
    for (auto j = 1; j <= nC; ++j) {
    	for (auto t = 1; t <= T; ++t) {
    		Yj(t) = Y(t, j);
		}
		dgp_obj.est_AR (resid_Yj, slope_Yj, SSR, Yj, lag_len);//fit Yj to an AR(lag_len) process, and obtain a sequence of residuals
		for (auto t = 1; t <= T-lag_len; ++t) {
			resid_Y(t, j) = resid_Yj(t);
		}
	}
	ofstream output;
    string output_filename = "./Application/file_out_T=" + std::to_string(T) + "_dy=" + std::to_string(nC) + "_lag_len=" + std::to_string(lag_len)
	                         + "_lag_smooth=" + std::to_string(lag_smooth) +  ".txt";
	output.open (output_filename.c_str(), ios::out);
	output << "El Himdi & Roy's (1997) (HR) test: " << endl;
	cout << "El Himdi & Roy's (1997) (HR) test: " << endl;
	Dep_tests dep_obj;
	int bandw = 10; //a bandwidth for El Himdi & Roy's (1997) statistic
	do {
	    output << "bandwidth = " << bandw << ": HR = " << dep_obj.do_ElHimdiRoyTest (bandw, resid_X, resid_Y) << endl;
	    bandw += 2;
	} while (bandw <= 30);
    int TL = 2;//truncation lag for kernel regressions
    double kernel_QDSum = 0., kernel_QRSum = 0., bandw_reg = pow(T, -0.6);//a bandwidth for nonparametric regressions
    Dist_corr obj_dc (X,Y);
    obj_dc.integrate_Kernel <bartlett_kernel> (&kernel_QDSum, &kernel_QRSum);//integrating a kernel function
    output << "The proposed distance correlation (DC) test: " << endl;
    cout << "The proposed distance correlation (DC) test: " << endl;
    do {
	    output << "truncation lag = " << TL << ": DC = " << obj_dc.do_Test <bartlett_kernel,epanechnikov_kernel> (TL, lag_smooth, kernel_QRSum, bandw_reg)  << endl;
	    TL += 1;
	} while (TL <= 15);
	output.close();

    /*CSVReader reader("./Application/data.csv");
	// Get the data from CSV File
	std::vector<std::vector<std::string> > dataList = reader.getData();
	// Print the content of row by row on screen
	for(std::vector<std::string> vec : dataList)
	{
		for(std::string data : vec)
		{
			std::cout<<data << " , ";
		}
		std::cout<<std::endl;
	}*/
    /********************************************************** Finish Calculating the Proposed Test Using Real Data ********************************************/
    /************************************************************************************************************************************************************/
    #endif //end comment

    /*Matrix alpha(3,1), beta(3,1), lambda(3,1), sigma(2,1);
    alpha(1) = 0.01;
    alpha(2) = 0.04;
    alpha(3) = 0.02;
    beta(1) = 0.7;
    beta(2) = 0.4;
    beta(3) = 0.5;
    lambda(1) = 0.;
    lambda(2) = -1;
    lambda(3) = 0.;
	sigma(1) = 1.5; // cf. Dgp::gen_MixedAR in dgp.h
	sigma(2) = 1.5; // cf. Dgp::gen_MixedAR in dgp.h
	int T = 50, bandW = 10;
	double rho = 0.1;
	Dgp dgp_obj;
	Matrix X(T, 1), Y1(T, 1), Y2(T, 1), resid_X(T-2, 1), slope_X(3, 1), resid_Y1(T-2, 1), slope_Y1(3, 1), resid_Y2(T-2, 1), slope_Y2(3, 1), resid_Y(T-2, 2);
	dgp_obj.gen_CMixedAR (X, Y1, alpha, beta, lambda, rho, 525235);//draw two independent Gaussian random samples for X and Y := (Y1, Y2)
	dgp_obj.gen_Resid (resid_X, slope_X, X);//estimate the d.g.p of X
	dgp_obj.gen_Resid (resid_Y1, slope_Y1, Y1);//estimate the d.g.p of Y1
	dgp_obj.gen_Resid (resid_Y2, slope_Y2, Y2);//estimate the d.g.p of Y2
	for (auto t = 1; t <= T-2; ++t) {
		resid_Y(t, 1) = resid_Y1(t);
		resid_Y(t, 2) = resid_Y2(t);
	}
	cout << X(10) << " , " << Y1(10) << endl;
	cout << Dep_tests:: do_ECFTest<bartlett_kernel> (bandW, X, Y1) << endl; */
	//Dep_tests dep_obj;
	//cout << dep_obj.do_ElHimdiRoyTest (bandW, resid_X, resid_Y) << endl;//calculate El Himdi & Roy's test statistic
    /*for (int t = 1; t <= T; ++t) {
    	Y(t,1) = Y1(t);
    	Y(t,2) = Y2(t);
	}
    Dist_corr dist_corr_obj (X,Y);
    cout << dist_corr_obj.do_Test <daniell_kernel> (TL, lag_smooth, 0.5, alpha, beta, lambda, sigma, rho, 523532523) << endl;*/
    //DWORD start = GetTickCount();
    /*gsl_rng * r;
    const gsl_rng_type * gen;//random number generator
    gsl_rng_env_setup();
    gen = gsl_rng_taus;
    r = gsl_rng_alloc(gen);
    gsl_rng_set(r, 143523);
    int T, T_max, d_x, d_y, number_sampl, nblocks, bsize, bandwidth, seed;
    double alpha = 1., ddep, pwr = 0.;
    number_sampl = 500;
    T = 50;
    T_max = 500;
    d_x = 4;
    d_y = 4;
    nblocks = 300;
    bandwidth = 5;
    bsize = 30;
    ddep = 0.;*/


     //# if 0 //begin comment
     /***********************************************************************************************************************************************/
     /******************************************** Start the Simulations for Other Tests: The Univariate Bilinear Case ********************************************/
     auto T = 200,  number_sampl = 500;
     double delta = 0.1, rho = 0.8;
	Matrix X(T,1), Y(T,1), alpha_X(6,1), alpha_Y(6,1);
     alpha_X(1) = 0.01;
     alpha_X(2) = 0.2;
     alpha_X(3) = 0.03;
     alpha_X(4) = -0.6;
     alpha_X(5) = -0.1;
     alpha_X(6) = 0.1;
     alpha_Y(1) = 0.04;
     alpha_Y(2) = 0.2;
     alpha_Y(3) = 0.04;
     alpha_Y(4) = -0.7;
     alpha_Y(5) = 0.1;
     alpha_Y(6) = 0.1;
	unsigned long seed = 856764325;
     string output_filename, size_filename, power_filename;
     ofstream output, size_out, pwr_out;
     Matrix REJF_Hong(2,1), REJF_ECFTest(2,1), REJF_Haugh(2,1), empir_CV_Hong(2,1), empir_CV_ECFTest(2,1), empir_CV_Haugh(2,1), asymp_CV_Hong(2,1), asymp_CV_Haugh(2,1);
     Matrix empir_REJF_Hong(2,1), asymp_REJF_Hong(2,1), empir_REJF_ECFTest(2,1), asymp_REJF_ECFTest(2,1), empir_REJF_Haugh(2,1), asymp_REJF_Haugh(2,1);
     asymp_CV_Hong(1) = 1.645; //5%-critical value from the standard normal distribution
     asymp_CV_Hong(2) = 1.28; //10%-critical value from the standard normal distribution
     int bandW = 5 /*10, 20, 25*/, choose_alt = 1;
     asymp_CV_Haugh = Dep_tests::asymp_CV_ChiSq (bandW);

    //*************************************************************using the Bartlett kernel****************************************************************************/
     output_filename = "./Results/NonGaussian/SN/Others/file_out_BL_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                     + "_rho=" + std::to_string(rho) + "_bartlett_kernel_univariate.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_BL_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
	                                + "_rho=" + std::to_string(rho) + "_bartlett_kernel_univariate.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_BL_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                     + "_rho=" + std::to_string(rho) + "_bartlett_kernel_univariate.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     output << "Lag smooth length = " << bandW << endl;
	//calculate empirical critical values and sizes
     Dep_tests::cValue <bartlett_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (REJF_Hong, REJF_ECFTest, REJF_Haugh, empir_CV_Hong, empir_CV_ECFTest,
                                                                                                                empir_CV_Haugh, alpha_X, alpha_Y, asymp_CV_Hong, asymp_CV_Haugh, number_sampl, T, bandW, delta, seed, size_out);
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_Hong(1) << " , "
                 << empir_CV_Hong(2) << ")" << endl;
     output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << asymp_CV_Hong(1) << " , "
                 << asymp_CV_Hong(2) << ")" << endl;
     output << "Hong's (1996) spectral test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << REJF_Hong(1) << " , " << REJF_Hong(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_ECFTest(1) << " , "
                 << empir_CV_ECFTest(2) << ")" << endl;
     output << "Hong's (2001) ecf-based test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << REJF_ECFTest(1) << " , " << REJF_ECFTest(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_Haugh(1) << " , "
                 << empir_CV_Haugh(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << asymp_CV_Haugh(1) << " , "
                 << asymp_CV_Haugh(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << REJF_Haugh(1) << " , " << REJF_Haugh(2)
                 << ")" << endl;
	//calculate rejection rates
	choose_alt = 1; //correlated errors
     Dep_tests::power_f<bartlett_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;

     choose_alt = 2; //uncorrelated but dependent errors
     Dep_tests::power_f<bartlett_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 3; //strongly dependent errors
     Dep_tests::power_f<bartlett_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	output.close();
     size_out.close();
     pwr_out.close();

    //***********************************************************using the Daniell kernel*************************************************************************
     output_filename = "./Results/NonGaussian/SN/Others/file_out_BL_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                    + "_rho=" + std::to_string(rho) + "_daniell_kernel_univariate.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_BL_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
	                               + "_rho=" + std::to_string(rho) + "_daniell_kernel_univariate.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_BL_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                    + "_rho=" + std::to_string(rho) + "_daniell_kernel_univariate.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     output << "Lag smooth length = " << bandW << endl;
	//calculate empirical critical values and sizes
     Dep_tests::cValue <daniell_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (REJF_Hong, REJF_ECFTest, REJF_Haugh, empir_CV_Hong, empir_CV_ECFTest,
                                                                                                                empir_CV_Haugh, alpha_X, alpha_Y, asymp_CV_Hong, asymp_CV_Haugh, number_sampl, T, bandW, delta, seed, size_out);
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_Hong(1) << " , "
                 << empir_CV_Hong(2) << ")" << endl;
     output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << asymp_CV_Hong(1) << " , "
                 << asymp_CV_Hong(2) << ")" << endl;
     output << "Hong's (1996) spectral test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << REJF_Hong(1) << " , " << REJF_Hong(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_ECFTest(1) << " , "
                 << empir_CV_ECFTest(2) << ")" << endl;
     output << "Hong's (2001) ecf-based test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << REJF_ECFTest(1) << " , " << REJF_ECFTest(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_Haugh(1) << " , "
                 << empir_CV_Haugh(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << asymp_CV_Haugh(1) << " , "
                 << asymp_CV_Haugh(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << REJF_Haugh(1) << " , " << REJF_Haugh(2)
                 << ")" << endl;
	//calculate rejection rates
	choose_alt = 1;
     Dep_tests::power_f<daniell_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 2;
     Dep_tests::power_f<daniell_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 3;
     Dep_tests::power_f<daniell_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	output.close();
     size_out.close();
     pwr_out.close();

    //******************************************************************using the QS kernel***********************************************************************
     output_filename = "./Results/NonGaussian/SN/Others/file_out_BL_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                     + "_rho=" + std::to_string(rho) + "_QS_kernel_univariate.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_BL_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
	                                + "_rho=" + std::to_string(rho) + "_QS_kernel_univariate.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_BL_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                     + "_rho=" + std::to_string(rho) + "_QS_kernel_univariate.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     output << "Lag smooth length = " << bandW << endl;
	//calculate empirical critical values and sizes
     Dep_tests::cValue <QS_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (REJF_Hong, REJF_ECFTest, REJF_Haugh, empir_CV_Hong, empir_CV_ECFTest,
                                                                                                                empir_CV_Haugh, alpha_X, alpha_Y, asymp_CV_Hong, asymp_CV_Haugh, number_sampl, T, bandW, delta, seed, size_out);
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_Hong(1) << " , "
                 << empir_CV_Hong(2) << ")" << endl;
     output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << asymp_CV_Hong(1) << " , "
                 << asymp_CV_Hong(2) << ")" << endl;
     output << "Hong's (1996) spectral test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << REJF_Hong(1) << " , " << REJF_Hong(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_ECFTest(1) << " , "
                 << empir_CV_ECFTest(2) << ")" << endl;
     output << "Hong's (2001) ecf-based test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << REJF_ECFTest(1) << " , " << REJF_ECFTest(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_Haugh(1) << " , "
                 << empir_CV_Haugh(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << asymp_CV_Haugh(1) << " , "
                 << asymp_CV_Haugh(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << REJF_Haugh(1) << " , " << REJF_Haugh(2)
                 << ")" << endl;
	//calculate rejection rates
	choose_alt = 1;
     Dep_tests::power_f<QS_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 2;
     Dep_tests::power_f<QS_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 3;
     Dep_tests::power_f<QS_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NL_Dgp::est_BL> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	output.close();
     size_out.close();
     pwr_out.close();
	/*************************************** Finish the Simulations for Other Tests: The Univariate Bilinear Case ***********************************************/
    /**********************************************************************************************************************************************/
	//#endif //end comment

	# if 0 //begin comment
     /***********************************************************************************************************************************************/
     /******************************************** Start the Simulations for Other Tests: The Univariate TAR Case ********************************************/
     auto T = 200,  number_sampl = 500;
     double delta = 0.1, rho = 0.8;
	Matrix X(T,1), Y(T,1), alpha_X(5,1), alpha_Y(5,1);
     alpha_X(1) = 0.01;
     alpha_X(2) = 0.7;
     alpha_X(3) = 0.1;
     alpha_X(4) = 0.1;
     alpha_X(5) = -0.3;
     alpha_Y(1) = 0.04;
     alpha_Y(2) = 0.4;
     alpha_Y(3) = 0.5;
     alpha_Y(4) = 0.1;
     alpha_Y(5) = -0.6;

	unsigned long seed = 856764325;
     string output_filename, size_filename, power_filename;
     ofstream output, size_out, pwr_out;
     Matrix REJF_Hong(2,1), REJF_ECFTest(2,1), REJF_Haugh(2,1), empir_CV_Hong(2,1), empir_CV_ECFTest(2,1), empir_CV_Haugh(2,1), asymp_CV_Hong(2,1), asymp_CV_Haugh(2,1);
     Matrix empir_REJF_Hong(2,1), asymp_REJF_Hong(2,1), empir_REJF_ECFTest(2,1), asymp_REJF_ECFTest(2,1), empir_REJF_Haugh(2,1), asymp_REJF_Haugh(2,1);
     asymp_CV_Hong(1) = 1.645; //5%-critical value from the standard normal distribution
     asymp_CV_Hong(2) = 1.28; //10%-critical value from the standard normal distribution
     int bandW = 5 /*10, 20, 25*/, choose_alt = 1;
     asymp_CV_Haugh = Dep_tests::asymp_CV_ChiSq (bandW);

    //*************************************************************using the Bartlett kernel****************************************************************************/
     output_filename = "./Results/NonGaussian/SN/Others/file_out_TAR_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                      + "_rho=" + std::to_string(rho) + "_bartlett_kernel_univariate.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_TAR_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                      + "_rho=" + std::to_string(rho) + "_bartlett_kernel_univariate.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_TAR_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                      + "_rho=" + std::to_string(rho) + "_bartlett_kernel_univariate.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     output << "Lag smooth length = " << bandW << endl;
	//calculate empirical critical values and sizes
     Dep_tests::cValue <bartlett_kernel, NL_Dgp::gen_TAR<NL_Dgp::gen_SN>, NL_Dgp::est_TAR> (REJF_Hong, REJF_ECFTest, REJF_Haugh, empir_CV_Hong, empir_CV_ECFTest,
                                                                                                                empir_CV_Haugh, alpha_X, alpha_Y, asymp_CV_Hong, asymp_CV_Haugh, number_sampl, T, bandW, delta, seed, size_out);
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_Hong(1) << " , "
                 << empir_CV_Hong(2) << ")" << endl;
     output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << asymp_CV_Hong(1) << " , "
                 << asymp_CV_Hong(2) << ")" << endl;
     output << "Hong's (1996) spectral test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << REJF_Hong(1) << " , " << REJF_Hong(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_ECFTest(1) << " , "
                 << empir_CV_ECFTest(2) << ")" << endl;
     output << "Hong's (2001) ecf-based test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << REJF_ECFTest(1) << " , " << REJF_ECFTest(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_Haugh(1) << " , "
                 << empir_CV_Haugh(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << asymp_CV_Haugh(1) << " , "
                 << asymp_CV_Haugh(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << REJF_Haugh(1) << " , " << REJF_Haugh(2)
                 << ")" << endl;
	//calculate rejection rates
	choose_alt = 1; //correlated errors
     Dep_tests::power_f<bartlett_kernel, NL_Dgp::gen_TAR<NL_Dgp::gen_SN>, NL_Dgp::est_TAR> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;

     choose_alt = 2; //uncorrelated but dependent errors
     Dep_tests::power_f<bartlett_kernel, NL_Dgp::gen_TAR<NL_Dgp::gen_SN>, NL_Dgp::est_TAR> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 3; //strongly dependent errors
     Dep_tests::power_f<bartlett_kernel, NL_Dgp::gen_TAR<NL_Dgp::gen_SN>, NL_Dgp::est_TAR> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	output.close();
     size_out.close();
     pwr_out.close();

    //***********************************************************using the Daniell kernel*************************************************************************
     output_filename = "./Results/NonGaussian/SN/Others/file_out_TAR_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                     + "_rho=" + std::to_string(rho) + "_daniell_kernel_univariate.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_TAR_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                     + "_rho=" + std::to_string(rho) + "_daniell_kernel_univariate.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_TAR_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                     + "_rho=" + std::to_string(rho) + "_daniell_kernel_univariate.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     output << "Lag smooth length = " << bandW << endl;
	//calculate empirical critical values and sizes
     Dep_tests::cValue <daniell_kernel, NL_Dgp::gen_TAR<NL_Dgp::gen_SN>, NL_Dgp::est_TAR> (REJF_Hong, REJF_ECFTest, REJF_Haugh, empir_CV_Hong, empir_CV_ECFTest,
                                                                                                                empir_CV_Haugh, alpha_X, alpha_Y, asymp_CV_Hong, asymp_CV_Haugh, number_sampl, T, bandW, delta, seed, size_out);
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_Hong(1) << " , "
                 << empir_CV_Hong(2) << ")" << endl;
     output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << asymp_CV_Hong(1) << " , "
                 << asymp_CV_Hong(2) << ")" << endl;
     output << "Hong's (1996) spectral test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << REJF_Hong(1) << " , " << REJF_Hong(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_ECFTest(1) << " , "
                 << empir_CV_ECFTest(2) << ")" << endl;
     output << "Hong's (2001) ecf-based test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << REJF_ECFTest(1) << " , " << REJF_ECFTest(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_Haugh(1) << " , "
                 << empir_CV_Haugh(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << asymp_CV_Haugh(1) << " , "
                 << asymp_CV_Haugh(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << REJF_Haugh(1) << " , " << REJF_Haugh(2)
                 << ")" << endl;
	//calculate rejection rates
	choose_alt = 1;
     Dep_tests::power_f<daniell_kernel, NL_Dgp::gen_TAR<NL_Dgp::gen_SN>, NL_Dgp::est_TAR> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 2;
     Dep_tests::power_f<daniell_kernel, NL_Dgp::gen_TAR<NL_Dgp::gen_SN>, NL_Dgp::est_TAR> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 3;
     Dep_tests::power_f<daniell_kernel, NL_Dgp::gen_TAR<NL_Dgp::gen_SN>, NL_Dgp::est_TAR> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	output.close();
     size_out.close();
     pwr_out.close();

    //******************************************************************using the QS kernel***********************************************************************
     output_filename = "./Results/NonGaussian/SN/Others/file_out_TAR_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                     + "_rho=" + std::to_string(rho) + "_QS_kernel_univariate.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_TAR_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                     + "_rho=" + std::to_string(rho) + "_QS_kernel_univariate.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_TAR_T=" + std::to_string(T) +  "_lag_smooth=" + std::to_string(bandW) + "_delta=" + std::to_string(delta)
                                     + "_rho=" + std::to_string(rho) + "_QS_kernel_univariate.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     output << "Lag smooth length = " << bandW << endl;
	//calculate empirical critical values and sizes
     Dep_tests::cValue <QS_kernel, NL_Dgp::gen_TAR<NL_Dgp::gen_SN>, NL_Dgp::est_TAR> (REJF_Hong, REJF_ECFTest, REJF_Haugh, empir_CV_Hong, empir_CV_ECFTest,
                                                                                                                empir_CV_Haugh, alpha_X, alpha_Y, asymp_CV_Hong, asymp_CV_Haugh, number_sampl, T, bandW, delta, seed, size_out);
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_Hong(1) << " , "
                 << empir_CV_Hong(2) << ")" << endl;
     output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << asymp_CV_Hong(1) << " , "
                 << asymp_CV_Hong(2) << ")" << endl;
     output << "Hong's (1996) spectral test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << REJF_Hong(1) << " , " << REJF_Hong(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_ECFTest(1) << " , "
                 << empir_CV_ECFTest(2) << ")" << endl;
     output << "Hong's (2001) ecf-based test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << REJF_ECFTest(1) << " , " << REJF_ECFTest(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are "  << "(" << empir_CV_Haugh(1) << " , "
                 << empir_CV_Haugh(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- critical value for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << asymp_CV_Haugh(1) << " , "
                 << asymp_CV_Haugh(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: 5%- and 10%- sizes for lag_smooth = " << bandW << " and delta= " << delta <<  " are " << "(" << REJF_Haugh(1) << " , " << REJF_Haugh(2)
                 << ")" << endl;
	//calculate rejection rates
	choose_alt = 1;
     Dep_tests::power_f<QS_kernel, NL_Dgp::gen_TAR<NL_Dgp::gen_SN>, NL_Dgp::est_TAR> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 2;
     Dep_tests::power_f<QS_kernel, NL_Dgp::gen_TAR<NL_Dgp::gen_SN>, NL_Dgp::est_TAR> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 3;
     Dep_tests::power_f<QS_kernel, NL_Dgp::gen_TAR<NL_Dgp::gen_SN>, NL_Dgp::est_TAR> (empir_REJF_Hong, asymp_REJF_Hong, empir_REJF_ECFTest, asymp_REJF_ECFTest,
                                                                                                                                                                                empir_REJF_Haugh, asymp_REJF_Haugh, alpha_X, alpha_Y, empir_CV_Hong,
                                                                                                                                                                                asymp_CV_Hong, empir_CV_ECFTest, asymp_CV_Hong, empir_CV_Haugh,
                                                                                                                                                                                asymp_CV_Haugh, number_sampl, T, bandW, delta, rho, choose_alt, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
     output << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	output << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     output << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	output << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     output << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	output << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     output << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
     cout << "Hong's (1996) spectral test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Hong(1) << " , " << empir_REJF_Hong(2)
                                                                                                                                                                         << ")" << endl;
	cout << "Hong's (1996) spectral test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Hong(1) << " , " << asymp_REJF_Hong(2)
                                                                                                                                                                           << ")" << endl;
     cout << "Hong's (2001) ecf-based test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_ECFTest(1) << " , "
                                                                                                                                                                           << empir_REJF_ECFTest(2) << ")" << endl;
	cout << "Hong's (2001) ecf-based test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_ECFTest(1) << " , "
	                                                                                                                                                                         << asymp_REJF_ECFTest(2) << ")" << endl;
     cout << "Haugh's (1976) Portmanteau test: empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF_Haugh(1) << " , "
                                                                                                                                                                                   << empir_REJF_Haugh(2) << ")" << endl;
	cout << "Haugh's (1976) Portmanteau test: asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF_Haugh(1) << " , "
                                                                                                                                                                                     << asymp_REJF_Haugh(2) << ")" << endl;
     cout << "----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
	output.close();
     size_out.close();
     pwr_out.close();
	/*************************************** Finish the Simulations for Other Tests: The Univariate TAR Case ***********************************************/
    /**********************************************************************************************************************************************/
	#endif //end comment


	#if 0 //begin comment
	/********************************************** Start the Simulations for El Himdi & Roy's test: The Bivariate Bilinear Case ***********************************/
    /************************************************************************************************************************************************/
     auto T = 100, number_sampl = 500, bandW = 1, choose_alt = 0;
     Matrix X(T,1), Y1(T,1), Y2(T,1), alpha_X(6,1), alpha_Y(6,2), delta(3,1);
     Matrix REJF_ElHimdiRoy(2,1), empir_CV_ElHimdiRoy(2,1), empir_REJF_ElHimdiRoy(2,1), asymp_REJF_ElHimdiRoy(2,1);
     alpha_X(1) = 0.01;
     alpha_X(2) = 0.2;
     alpha_X(3) = 0.03;
     alpha_X(4) = -0.6;
     alpha_X(5) = -0.1;
     alpha_X(6) = 0.1;
     alpha_Y(1,1) = 0.04;
     alpha_Y(2,1) = 0.2;
     alpha_Y(3,1) = 0.04;
     alpha_Y(4,1) = -0.7;
     alpha_Y(5,1) = 0.1;
     alpha_Y(6,1) = 0.1;
     alpha_Y(1,2) = 0.05;
     alpha_Y(2,2) = 0.8;
     alpha_Y(3,2) = -0.05;
     alpha_Y(4,2) = -0.5;
     alpha_Y(5,2) = -0.1;
     alpha_Y(6,2) = 0.1;
     delta(1) = 0.1;
     delta(2) = 0.9;
     delta(3) = -0.1;
     double rho12 = -0.5, rho13 = 0.2;
     unsigned long seed = 856764325;
     string output_filename, size_filename, power_filename;
     ofstream output, size_out, pwr_out;
     bandW = 5;
     output << "Lag smooth length = " << bandW << endl;
     output_filename = "./Results/NonGaussian/SN/Others/file_out_BL_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_BL_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_BL_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     //calculate empirical critical values and sizes
	Matrix asymp_CV_ElHimdiRoy = Dep_tests::asymp_CV_ChiSq2 (bandW); //obtain 5%- and 10%- asymptotic critical values for the test
     Dep_tests::cValue <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (REJF_ElHimdiRoy, empir_CV_ElHimdiRoy, alpha_X, alpha_Y, delta, asymp_CV_ElHimdiRoy,
                                                                                                                                                          number_sampl, T, bandW, seed, size_out);
     output << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     output << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     //calculate rejection rates
     choose_alt = 1; //errors are uncorrelated but dependent
     Dep_tests::power_f <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 2; //errors are corrrelated  (thus dependent)
     Dep_tests::power_f <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output.close();
     size_out.close();
     pwr_out.close();

	//================================================================================================================================
     bandW = 10;
     output << "Lag smooth length = " << bandW << endl;
     output_filename = "./Results/NonGaussian/SN/Others/file_out_BL_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_BL_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_BL_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     //calculate empirical critical values and sizes
	asymp_CV_ElHimdiRoy = Dep_tests::asymp_CV_ChiSq2 (bandW);//obtain 5%- and 10%- asymptotic critical values for the test
     Dep_tests::cValue <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (REJF_ElHimdiRoy, empir_CV_ElHimdiRoy, alpha_X, alpha_Y, delta, asymp_CV_ElHimdiRoy,
                                                                                                                                                          number_sampl, T, bandW, seed, size_out);
     output << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     output << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     //calculate rejection rates
     choose_alt = 1; //errors are uncorrelated but dependent
     Dep_tests::power_f <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 2; //errors are corrrelated  (thus dependent)
     Dep_tests::power_f <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output.close();
     size_out.close();
     pwr_out.close();

    //============================================================================================================================================================
     bandW = 20;
     output << "Lag smooth length = " << bandW << endl;
     output_filename = "./Results/NonGaussian/SN/Others/file_out_BL_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_BL_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_BL_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     //calculate empirical critical values and sizes
	asymp_CV_ElHimdiRoy = Dep_tests::asymp_CV_ChiSq2 (bandW);//obtain 5%- and 10%- asymptotic critical values for the test
     Dep_tests::cValue <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (REJF_ElHimdiRoy, empir_CV_ElHimdiRoy, alpha_X, alpha_Y, delta, asymp_CV_ElHimdiRoy,
                                                                                                                                                          number_sampl, T, bandW, seed, size_out);
     output << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     output << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     //calculate rejection rates
     choose_alt = 1; //errors are uncorrelated but dependent
     Dep_tests::power_f <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 2; //errors are corrrelated  (thus dependent)
     Dep_tests::power_f <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output.close();
     size_out.close();
     pwr_out.close();

    //============================================================================================================================================================
     bandW = 25;
     output << "Lag smooth length = " << bandW << endl;
     output_filename = "./Results/NonGaussian/SN/Others/file_out_BL_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_BL_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_BL_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     //calculate empirical critical values and sizes
	asymp_CV_ElHimdiRoy = Dep_tests::asymp_CV_ChiSq2 (bandW);//obtain 5%- and 10%- asymptotic critical values for the test
     Dep_tests::cValue <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (REJF_ElHimdiRoy, empir_CV_ElHimdiRoy, alpha_X, alpha_Y, delta, asymp_CV_ElHimdiRoy,
                                                                                                                                                          number_sampl, T, bandW, seed, size_out);
     output << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     output << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     //calculate rejection rates
     choose_alt = 1; //errors are uncorrelated but dependent
     Dep_tests::power_f <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 2; //errors are corrrelated  (thus dependent)
     Dep_tests::power_f <NL_Dgp::gen_Bilinear<NL_Dgp::gen_TriSN>, NL_Dgp::est_BL> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output.close();
     size_out.close();
     pwr_out.close();

    /***************************************** Finish the Simulations for El Himdi & Roy's test: The Bivariate Bilinear Case ****************************************/
    /************************************************************************************************************************************************/
	#endif //end comment

	#if 0 //begin comment
	/********************************************** Start the Simulations for El Himdi & Roy's test: The Bivariate TAR Case ***********************************/
    /************************************************************************************************************************************************/
     auto T = 100, number_sampl = 500, bandW = 1, choose_alt = 0;
     Matrix X(T,1), Y1(T,1), Y2(T,1), alpha_X(5,1), alpha_Y(5,2), delta(3,1);
     Matrix REJF_ElHimdiRoy(2,1), empir_CV_ElHimdiRoy(2,1), empir_REJF_ElHimdiRoy(2,1), asymp_REJF_ElHimdiRoy(2,1);

     alpha_X(1) = 0.01; //define the AR coefficients
     alpha_X(2) = 0.7;
     alpha_X(3) = 0.1;
     alpha_X(4) = -0.6;
     alpha_X(5) = 0.3;
     alpha_Y(1,1) = 0.04;
     alpha_Y(2,1) = 0.4;
     alpha_Y(3,1) = 0.5;
     alpha_Y(4,1) = 0.1;
     alpha_Y(5,1) = -0.6;
     alpha_Y(1,2) = 0.01;
     alpha_Y(2,2) = -0.2;
     alpha_Y(3,2) = 0.1;
     alpha_Y(4,2) = 0.05;
     alpha_Y(5,2) = 0.4;
     delta(1) = 0.1;
     delta(2) = 0.9;
     delta(3) = -0.1;
     double rho12 = -0.5, rho13 = 0.2;
     unsigned long seed = 856764325;
     string output_filename, size_filename, power_filename;
     ofstream output, size_out, pwr_out;
     bandW = 5;
     output << "Lag smooth length = " << bandW << endl;
     output_filename = "./Results/NonGaussian/SN/Others/file_out_TAR_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_TAR_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_TAR_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     //calculate empirical critical values and sizes
	Matrix asymp_CV_ElHimdiRoy = Dep_tests::asymp_CV_ChiSq2 (bandW); //obtain 5%- and 10%- asymptotic critical values for the test
     Dep_tests::cValue <NL_Dgp::gen_TAR<NL_Dgp::gen_TriSN>, NL_Dgp::est_TAR> (REJF_ElHimdiRoy, empir_CV_ElHimdiRoy, alpha_X, alpha_Y, delta, asymp_CV_ElHimdiRoy,
                                                                                                                                                          number_sampl, T, bandW, seed, size_out);
     output << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     output << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     //calculate rejection rates
     choose_alt = 1; //errors are uncorrelated but dependent
     Dep_tests::power_f <NL_Dgp::gen_TAR<NL_Dgp::gen_TriSN>, NL_Dgp::est_TAR> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 2; //errors are corrrelated  (thus dependent)
     Dep_tests::power_f <NL_Dgp::gen_TAR<NL_Dgp::gen_TriSN>, NL_Dgp::est_TAR> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output.close();
     size_out.close();
     pwr_out.close();

	//================================================================================================================================
     bandW = 10;
     output << "Lag smooth length = " << bandW << endl;
     output_filename = "./Results/NonGaussian/SN/Others/file_out_TAR_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_TAR_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_TAR_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     //calculate empirical critical values and sizes
     asymp_CV_ElHimdiRoy = Dep_tests::asymp_CV_ChiSq2 (bandW); //obtain 5%- and 10%- asymptotic critical values for the test
     Dep_tests::cValue <NL_Dgp::gen_TAR<NL_Dgp::gen_TriSN>, NL_Dgp::est_TAR> (REJF_ElHimdiRoy, empir_CV_ElHimdiRoy, alpha_X, alpha_Y, delta, asymp_CV_ElHimdiRoy,
                                                                                                                                                          number_sampl, T, bandW, seed, size_out);
     output << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     output << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     //calculate rejection rates
     choose_alt = 1; //errors are uncorrelated but dependent
     Dep_tests::power_f <NL_Dgp::gen_TAR<NL_Dgp::gen_TriSN>, NL_Dgp::est_TAR> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 2; //errors are corrrelated  (thus dependent)
     Dep_tests::power_f <NL_Dgp::gen_TAR<NL_Dgp::gen_TriSN>, NL_Dgp::est_TAR> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output.close();
     size_out.close();
     pwr_out.close();

	//================================================================================================================================
     bandW =  20;
     output << "Lag smooth length = " << bandW << endl;
     output_filename = "./Results/NonGaussian/SN/Others/file_out_TAR_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_TAR_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_TAR_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     //calculate empirical critical values and sizes
	asymp_CV_ElHimdiRoy = Dep_tests::asymp_CV_ChiSq2 (bandW); //obtain 5%- and 10%- asymptotic critical values for the test
     Dep_tests::cValue <NL_Dgp::gen_TAR<NL_Dgp::gen_TriSN>, NL_Dgp::est_TAR> (REJF_ElHimdiRoy, empir_CV_ElHimdiRoy, alpha_X, alpha_Y, delta, asymp_CV_ElHimdiRoy,
                                                                                                                                                          number_sampl, T, bandW, seed, size_out);
     output << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     output << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     //calculate rejection rates
     choose_alt = 1; //errors are uncorrelated but dependent
     Dep_tests::power_f <NL_Dgp::gen_TAR<NL_Dgp::gen_TriSN>, NL_Dgp::est_TAR> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 2; //errors are corrrelated  (thus dependent)
     Dep_tests::power_f <NL_Dgp::gen_TAR<NL_Dgp::gen_TriSN>, NL_Dgp::est_TAR> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output.close();
     size_out.close();
     pwr_out.close();

	//================================================================================================================================
     bandW = 25;
     output << "Lag smooth length = " << bandW << endl;
     output_filename = "./Results/NonGaussian/SN/Others/file_out_TAR_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
	size_filename = "./Results/NonGaussian/SN/Others/size_out_TAR_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     power_filename = "./Results/NonGaussian/SN/Others/power_out_TAR_T=" + std::to_string(T) +  "_bandW=" + std::to_string(bandW) + "_delta=" + std::to_string(delta(1)) + "_"
                                    + std::to_string(delta(2)) + "_" + std::to_string(delta(3)) + "_HRTest.txt";
     output.open (output_filename.c_str(), ios::out);
     size_out.open (size_filename.c_str(), ios::out);
     pwr_out.open (power_filename.c_str(), ios::out);
     //calculate empirical critical values and sizes
	asymp_CV_ElHimdiRoy = Dep_tests::asymp_CV_ChiSq2 (bandW); //obtain 5%- and 10%- asymptotic critical values for the test
     Dep_tests::cValue <NL_Dgp::gen_TAR<NL_Dgp::gen_TriSN>, NL_Dgp::est_TAR> (REJF_ElHimdiRoy, empir_CV_ElHimdiRoy, alpha_X, alpha_Y, delta, asymp_CV_ElHimdiRoy,
                                                                                                                                                          number_sampl, T, bandW, seed, size_out);
     output << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     output << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- empirical critical values for bandW = " <<  bandW << ":  " << "(" << empir_CV_ElHimdiRoy(1) << " , " << empir_CV_ElHimdiRoy(2) << ")" << endl;
     cout << "5%- and 10%- sizes for bandW = " <<  bandW << ":  " << "(" << REJF_ElHimdiRoy(1) << " , " << REJF_ElHimdiRoy(2) << ")" << endl;
     //calculate rejection rates
     choose_alt = 1; //errors are uncorrelated but dependent
     Dep_tests::power_f <NL_Dgp::gen_TAR<NL_Dgp::gen_TriSN>, NL_Dgp::est_TAR> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     choose_alt = 2; //errors are corrrelated  (thus dependent)
     Dep_tests::power_f <NL_Dgp::gen_TAR<NL_Dgp::gen_TriSN>, NL_Dgp::est_TAR> (empir_REJF_ElHimdiRoy, asymp_REJF_ElHimdiRoy, alpha_X, alpha_Y, delta,
                                                                                                                                                           empir_CV_ElHimdiRoy, asymp_CV_ElHimdiRoy, rho12, rho13, choose_alt, number_sampl,
                                                                                                                                                           T, bandW, seed, pwr_out);
     output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output << "choose_alt = " << choose_alt << endl;
	output << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	output << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     cout << "choose_alt = " << choose_alt << endl;
	cout << "5%- and 10% - empirical rejection rates for bandW = " << bandW << ": " << "(" << empir_REJF_ElHimdiRoy(1) << " , " << empir_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "5%- and 10% - asymptotic rejection rates for bandW = " << bandW << ": " << "(" << asymp_REJF_ElHimdiRoy(1) << " , " << asymp_REJF_ElHimdiRoy(2) << ")" << endl;
	cout << "-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------" << endl;
     output.close();
     size_out.close();
     pwr_out.close();

     /***************************************** Finish the Simulations for El Himdi & Roy's test: The Bivariate TAR Case ****************************************/
     /************************************************************************************************************************************************/
	#endif //end comment

	/*Matrix alpha_x(2,1), alpha_y(2,1), beta_x(2,1), beta_y(2,1);
	alpha_x(1) = 0.001;
	alpha_x(2) = -0.002;
	beta_x(1) = 0.4;
	beta_x(2) = 0.1;
	alpha_y(1) = -0.001;
	alpha_y(2) = 0.002;
	beta_y(1) = 0.9;
	beta_y(2) = 0.78;
    Dgp dgp_obj (alpha_x, alpha_y, beta_x, beta_y);
    //Dgp dgp_obj;
    //dgp_obj.gen_MixedAR (X, Y, alpha, beta, lambda, rho, 543590823);
    Matrix X(50,2), Y(50,2);
    dgp_obj.gen_AR1 (X, Y, 0., 55235);*/
    /*int i = 1, TL = 10;
    while (i <= TL) {
    	x1(i,1) = X(TL-i+1,1);
    	x1(i,2) = X(TL-i+1,2);
    	x2(i,1) = X(TL-i+4,1);
    	x2(i,2) = X(TL-i+4,2);
    	++i;
	}
	x0(1,1) = 0.5;
	x0(1,2) = 0.01;*/
	//NReg nreg_obj;
	//NReg nreg_obj;
	//int lag = -2;
	//int lag_smooth = 10;
	/*int number_sampl = 500;
	Matrix sigma(2,1);
	sigma(1) = sqrt(2);
	sigma(2) = sqrt(0.5 + pow(rho, 2.) * 1.5);
	string output_filename, power_filename;
    power_filename =  "test_power_statistics.txt";
    ofstream pwr_out;
    pwr_out.open (power_filename.c_str(), ios::out);
    Power obj_power;
    double reject_rate = 0.;
    reject_rate = obj_power.power_f <bartlett_kernel> (number_sampl, T, TL, lag_smooth, alpha, beta, lambda, sigma, rho, 0.95, 645345, pwr_out);
	cout << reject_rate << endl;*/
	//cout << "rho = " << rho <<": The value of the test statistic is " << dist_corr_obj.do_Test <bartlett_kernel> (TL, lag_smooth, alpha, beta, lambda, sigma)<< endl;
    //cout << "the denominator = " << nreg_obj.weight <epanechnikov_kernel> (X, x1, TL, 0.03) << endl;
    //cout << "the distance covariance test = " << nreg_obj.do_Test <bartlett_kernel,epanechnikov_kernel> (X, Y, 10, 10, 0.03) << endl;
    //cout << "the regression function = " << nreg_obj.var_Ux_ts <triangle_kernel> (X, x1, x2, x0, x0, TL, 0.03) << endl;
    //please do not comment out the lines below.
    //time = ((double) clock())/((double) CLOCKS_PER_SEC);
    time = std::chrono::high_resolution_clock::now();
    //output << "Elapsed time = " << (time-timelast)/60 << " minutes" << endl;
    //cout << "Elapsed time = " << (time-timelast)/60 << " minutes" << endl;
    //output << "This program took " << std::chrono::duration_cast <std::chrono::seconds> (time-timelast).count() << " seconds to run.\n";
    cout << "This program took " << std::chrono::duration_cast <std::chrono::milliseconds> (time-timelast).count() << " milliseconds to run.\n";
    //output.close ();
    //pwr_out.close ();
    //gsl_rng_free (r);
    #if defined(_WIN64) || defined(_WIN32)
    system("PAUSE");
    #endif
    return 0;
}