Final.Rmd

---
title: "Final"
author: "Leonid Maksymenko"
date: "5/15/2021"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(quantmod)
library(TSA)
library(forecast)
```

```{r}
#a
Stock = getSymbols('GME', from = "2018-01-01", to = "2021-01-01", src = "yahoo", auto.assign=FALSE)
Stockadj = Stock$GME.Adjusted
Stocklog = dailyReturn(Stockadj, type = "log")

plot(Stockadj, col = 'red', main="GME Adjusted Close", xlab = 'Date', ylab = 'Price in $')
plot(Stocklog, col = 'red', main="GME Adjusted Close Log Returns", xlab = 'Date', ylab = 'Return in %')
```

```{r}
#b
Stockvec = as.vector(Stockadj)
testing = tail(Stockvec, 5)
training = head(Stockvec, -5)
len = length(training)

#add legends, wtf do the instructions mean???
plot(tail(training, 5), 
     col = 'black', 
     main="GME Adjusted Close", xlab = 'Date', ylab = 'Price in $', 
     ylim = c(-25,25), 
     xlim = c(1,10),
     type = 'l')
lines(testing, x = c(5,6,7,9, 10), col = 'red')
legend("bottomleft",
       legend = c('Last 5 days Training', 'Testing'),
       col = c('black', 'red'),
       pch = 15
)

```

```{r}
#c

acf(training)
pacf(training)


#AR model
armodel = ar(training ,method="mle")
armodel # order 9 best
#remaking the model using arima because ar function doesnt work with predict function
armodel = arima(training, order = c(9,0,0))

###NOT WORKING###
#maxord = 30
#armodel.aic=c()
#for (q in 1:maxord){
#  try(
#    (armodel.aic = append(model.aic, arima(training,order=c(q,0,0))$aic))
#  )
#}
#arorder = match( min(model.aic), model.aic)
#arorder

#MA model
maxord = 30
mamodel.aic=c()
for (q in 1:maxord){
  mamodel.aic = append(mamodel.aic, arima(training,order=c(0,0,q))$aic)
}
maorder = match( min(mamodel.aic), mamodel.aic)
maorder # best order is 27
mamodel = arima(training, order = c(0,0,maorder))

#ARMA model

#combining the 2 models to form the arma
arma = auto.arima(training)

```

```{r}
#d
#predict the last 5 days
predictionar = predict(armodel,5)
predictionar = as.vector(predictionar$pred)
predictionar#20.68158 20.59473 20.32544 20.15361 19.95017

predictionma = predict(mamodel,5)
predictionma = as.vector(predictionma$pred)
predictionma#21.20355 21.32604 21.78675 22.20136 22.35209

predictionarma = predict(arma,5)
predictionarma = as.vector(predictionarma$pred)
predictionarma#23.24346 25.05011 27.33734 29.35813 31.52664
```

```{r}
#e
#compute sum of squared errors
errorar = sum((testing - predictionar)^2)
errorar #3.363669

errorma = sum((testing - predictionma)^2)
errorma #28.00169

errorarma = sum((testing - predictionarma)^2)
errorarma #352.2963

#ar model had the best prediction
```

Interview Problem

```{r}
#import csv
Final_Data = read.csv("Final_Data.csv",header=T)

#simple linear regression
linmod <- lm(y~x, data = Final_Data)
resid <- linmod$residuals
  #assumptions violated?
    
    par(mfrom = c(2,2))
    plot(linmod)
    
    #linearity of data
      #Residuals v. Fitted used to check linear relationship assumptions. Horizontal line without distinct patterns implies linear relationship 
        #good
    
    #normality of residuals
      #Normal QQ Checks the normality of the residuals, if they follow the diagonal line that is good
        #good
      #Can also use normality tests
  
    #Homogeneity of residuals variance
      #Scale-Location Checks homogeneity of the variance of the residuals (homoscedasticity) 
        #line horizontal good but points arent every evenly spread
      
    #extra?
      #residuals v Leverage checks for extreme data point that could skew the regression
        #The line looks straight are there are no outlier points outside the Cook's distance that heavily influence the data
    
    #independence of residual error terms
      #testing for autocorrelation
      acf(resid)
      #may be concers with independence

```


```{r}
#c

#brute force armiax model(p,0,q) for p and q 0 to 3
aic.matrix = function(data, ar_order, ma_order)
{
  AIC_matrix <- matrix(NA, nrow = ar_order+1, ncol = ma_order+1)
  for(i in 0 : ar_order)
  {
    for(j in 0 : ma_order)
    {
      tem <- tryCatch(arimax(data, order = c(i, 0, j))$aic, 
                      error = function(cond)
                      {
                        message(cond)
                        message(". AR: ", i, "; MA: ",j)
                        return (NA)
                      }
      )
      
      AIC_matrix[i+1, j+1] <- tem
    }
  }
  AIC_matrix
}

matrix = aic.matrix(resid, 3, 3)
matrix
which(matrix == min(na.omit(matrix)), arr.ind = TRUE) -1
#best model is 1,0,1
```

```{r}
#d
#make the model
arimaxModel <- arimax(resid,order = c(1,0,1))
# Check independence of residuals

tsdiag(arimaxModel)          
Box.test(arimaxModel$resid,lag=10,type='Ljung') 
#the p value is very high, we do not reject the null (white noise), thus, residuals are white noise
```

         [,1]     [,2]     [,3]     [,4]
[1,] 12503.69 11127.71 10958.74 10943.89
[2,] 10979.27 10937.29 10939.19 10940.91
[3,] 10938.24 10939.21 10941.13 10942.77
[4,] 10939.09 10941.10 10942.84 10944.78