#take home exam EE435_6004641699

library(vars)
library(abind)
library(xts)
library(MTS)
library(quantmod)
library(tseries)
library(timeSeries)
library(timeDate)
library(urca)

getSymbols("IPDCONGD",src="FRED")
dim(IPDCONGD)
tail(IPDCONGD)

getSymbols("IPNCONGD",src="FRED")
dim(IPNCONGD)

getSymbols("IPBUSEQ",src="FRED")
dim(IPBUSEQ)

getSymbols("IPMAT",src="FRED")
dim(IPMAT)

IP= cbind(as.numeric(IPDCONGD),as.numeric(IPNCONGD),as.numeric(IPBUSEQ),as.numeric(IPMAT[-c(1:96)]))
dim(IP)

colnames(IP) = c("IPD","IPN","IPB","IPM")


#question 1-1
zt=diffM(log(IP))*100

par(mar=c(1,1,1,1))
ts.plot(zt)

MTSplot(zt)
ccm(zt)
adf=adf.test(diffM(log(as.numeric(IP))))


#question 1-2
VARorder(zt)
m1=VAR(zt,2)
m11 = refVAR(m1,thres=1.645)
par("mar")
par(mar=c(1,1,1,1))
MTSdiag(m11)



#question 1-3
detach("package:MTS", unload = TRUE)



varfit=VAR(zt,p=2)
summary(varfit)


impresp=irf(varfit)
plot(impresp)


#question 1-4
fevd(varfit,n.ahead=6)



#question 1-5
varfit.prd=predict(varfit,n.ahead=1,ci=0.95)
varfit.prd=predict(varfit,n.ahead=2,ci=0.95)
varfit.prd=predict(varfit,n.ahead=3,ci=0.95)
varfit.prd=predict(varfit,n.ahead=4,ci=0.95)
varfit.prd=predict(varfit,n.ahead=5,ci=0.95)
varfit.prd=predict(varfit,n.ahead=6,ci=0.95)

detach("package:vars", unload = TRUE)
require(MTS)
VARpred(m11,6,orig=879)




#Question 2
#forecast return and volatilities model

library(ggplot2)
library(caTools)
library(dygraphs)
library(xts)
library(forecast)
library(fGarch)
library(tseries)
library(ggplot2)

getSymbols("ETH-USD",from="2015-01-01",to="2021-05-24")
head(`ETH-USD`)
da = `ETH-USD`

price = da[,6]
price = as.ts(price)

plot(price,type="l")
logprice=log(price)
plot(logprice)
logreturn=diff(log(price))
plot(logreturn)
typeof(logreturn)


da$data.Date = as.Date(da$c[,0])


acf(logreturn)
pacf(logreturn)

adf.test(logreturn)
fit1 = auto.arima(logreturn, trace = TRUE, test = "kpss", ic = "bic")
Box.test(fit1$residuals, lag = 12, type = "Ljung-Box")
acf(fit1$residuals^2)

tsdisplay(fit1$residuals)
tsdiag(fit1)

model=garchFit(~arma(1,0)+garch(1,1), data=diff(da$sqrt), trace=F, cond.dist ='std')

summary (model)

resid=residuals(model, standardize=T)
Box.test(resid)
plot(resid,type='l', main="Residual plot for model")
Box.test(resid^2)
tsdisplay(resid^2)
pred=predict(model,n.ahead=15,plot=TRUE,crit_val =1)




#Question 3

#import dataset in environment


daa = NAEXKP01CAQ189S[,2]
dab = CLVMNACSCAB1GQUK[,2]
dac = GDPC1[,2]

GDP = cbind(daa$NAEXKP01CAQ189S,dab$CLVMNACSCAB1GQUK,dac$GDPC1)

colnames(GDP) <- c("UK","CA","US")
ztx = diff(long(GDP))

VARorder(ztx)

mx = VAR(ztx,1)
MTSdiag(mx)

my = refVAR(mx,thres=1.645)
MTSdiag(my)



impresp1=irf(varfit)
plot(impresp1)

impresp2=irf(varfit)
plot(impresp2)

VARfore(mx, n.ahead = 20)
VARfore(my, n.ahead = 20)
fevd(mx, n.ahead = 20)
fevd(my, n.ahead = 20)