library(urca)
#library(fUnitRoots)
library(urca)
library(vars)
library(aod)
library(zoo)
library(tseries)
data(denmark)

lapply(2:5,function(i)adf.test(denmark[[i]])) # I haven't gone in details over these
lapply(2:5,function(i)adf.test(diff(denmark[[i]]))) # I haven't gone in details over these; you need to check but I assume that they are of I(1)
VARselect(denmark[,2:4],lag=20,type="both") #something like lag 11 is prefered
V.11<-VAR(denmark[,2:4],p=11,type="both")
serial.test(V.11)
1/roots(V.11)[[1]]
plot(stability(V.11))
V.12<-VAR(denmark[,2:4],p=12,type="both") # I haven't gone in details over these (add 1 lag as in the linked website)
V.12$varresult
summary(V.12)

#Wald-test (H0: LRY does not Granger-cause LRM)
wald.test(b=coef(V.12$varresult[[1]]), Sigma=vcov(V.12$varresult[[1]]), Terms=seq(2,33,3))


#Wald-test (H0: LPY does not Granger-cause LRM)
wald.test(b=coef(V.12$varresult[[1]]), Sigma=vcov(V.12$varresult[[1]]), Terms=seq(3,33,3))


#Wald-test (H0: LRM does not Granger-cause LRY)
wald.test(b=coef(V.12$varresult[[2]]), Sigma=vcov(V.12$varresult[[2]]), Terms=seq(1,33,3))

#Wald-test (H0: LPY does not Granger-cause LRY)
wald.test(b=coef(V.12$varresult[[2]]), Sigma=vcov(V.12$varresult[[2]]), Terms=seq(3,33,3))

#Wald-test (H0: LRM does not Granger-cause LPY)
wald.test(b=coef(V.12$varresult[[3]]), Sigma=vcov(V.12$varresult[[3]]), Terms=seq(1,33,3))


#Wald-test (H0: LRY does not Granger-cause LPY)
wald.test(b=coef(V.12$varresult[[3]]), Sigma=vcov(V.12$varresult[[3]]), Terms=seq(2,33,3))