HamiltonFilter.inp

#clear
set messages off
set echo off

####################################################################################
#
#		'Hamilton Filter'
#		based on J. Hamilton's paper
#
#		"Why You Should Never Use the Hodrick-Prescott Filter"
#	 	(revised version Oct. 2016)
#		URL: http://econweb.ucsd.edu/~jhamilto/hp.pdf
#		Blog1: http://econbrowser.com/archives/2016/08/why-you-should-never-use-the-hodrick-prescott-filter
#		Blog2: http://fxdiebold.blogspot.de/2016/08/on-evils-of-hodrick-prescott-detrending.html
#			
#	Hamilton suggests to rely on the population linear
#	projection of y t+h on a constant and the p most recent values
#	of y as of date t.
#
#
#	Input:
#		y		- series, variable to filter
#		hval	- int, 'h' projection horizon. Recommended: annual: h=2, quarterly:h=8, monthly:h=24
#					NOTE: This wipes out any cycles with frequency of exactly one year
#		pval 	- int, 'p' is the flexibility parameter; if D^d(y_t) (D:difference operator)
#					is stationary of some value d,  choose p>d, Hamilton uses p=4 for quarterly data.
#		verb	- int, 0:print NO output, 1:print output
#
#
####################################################################################

function series hamfilt(series y,
    int hval, int pval, int verb[0:1:0])
    
    start = hval
    ende = hval + pval -1
    if verb==0
        string opt="--quiet"
    else
        string opt=""
    endif    
    ols y const y(-hval to -ende) @opt
    series cycle = $uhat
    smpl ($t1 + hval + pval) ;
    return cycle
end function


/*
#----------
# Example 
#----------
# Load Hamilton's data
open \
  /home/at/ownCloud/gretl_script/ExternalProgs/Hamilton2016_OnHPFilter/Hamilton_RATS/employment.csv
setobs 4 1947:1 --time-series
delete v1
rename v2 nfp
rename v3 nfp_nsa
setinfo nfp --description="Employment, SA"
setinfo nfp_nsa --description="Employment, NSA"
series nfp_log = log(nfp)*100

# Set parameters
scalar pval = 4
scalar hval = 8

# Run procedure
series nfp_hamfilt_SA = hamfilt(nfp_log,hval,pval)

# Compare with standard HP-Filter
series nfp_hpfilt_SA = hpfilt(nfp_log)

# Plot both resulting cyclical components
gnuplot nfp_hamfilt_SA nfp_hpfilt_SA --with-lines --time-series --output=display

# Plot (P)ACF for both series
corrgm nfp_hamfilt_SA --plot=display
corrgm nfp_hpfilt_SA --plot=display
*/