# R code for VAR series

install.packages("vars")
library(vars)

T<-140


U1<-ts(rnorm(T), frequency=4, start=c(1970,1))
U2<-ts(rnorm(T), frequency=4, start=c(1970,1))


ts.plot(U1,ylab="Random walks", col=c("blue"))
lines(U2,ylab="Random walks", col=c("red"))

X1<-0*c(1:T);X2<-0*c(1:T)
for (t in 1:(T-1)) {
  X1[t+1]<-0.45*X1[t]+0.45*X2[t]+U1[t]
  X2[t+1]<-0.25*X1[t]+0.55*X2[t]+U2[t]
  }


ts.plot(X1,ylab="vars", col=c("blue"))
lines(X2, col=c("red"))

U<-cbind(U1,U2)
X<-cbind(X1,X2)

#to look for the best order
VARselect(X)
#Then call VAR with this best order p
VAR(X,p=1)

#or alternatively choose a criteria and let VAR choose the best order accordingly.
res<-VAR(X,ic="AIC",lag.max=5,type="none") #type defines the deterministic model (none, const, trend, both)
summary(res)

#Validation: autocorrelation
autocor.test<-serial.test(res)
autocor.test
plot(autocor.test,names="X1")

#Validation: heteroscedasticity
arch.test(res)

#Validation: normality
normality.test(res)


#Causality
causality(res,cause="X1")