#install.packages("urca")
library(urca)

set.seed(123)
x2<-u2<-rnorm(300)
for(t in 2:300) x2[t]=0.5+x2[t-1]+u2[t]
#x2.ts<-ts(x2)

set.seed(1234)
u1<-v<-rnorm(300)
for(t in 2:300) u1[t]=0.9*u1[t-1]+v[t]
#u1.ts<-ts(u1)

set.seed(12345)
x1<-z<-rnorm(300)
for(t in 2:300) x1[t]=4.5+x2[t]+u1[t]
#x1.ts<-ts(x1)

n=length(x1)
tr=1:n
tr
# Unit Root Test

(dx1=diff(x1))
(n1=(length(dx1)))
(lagx1=x1[2:n1])
(tr1=2:n1)
ndx1=dx1[2:n1]
ndx1
lagdx1=dx1[1:n1-1]

summary(lm(ndx1~tr1+lagx1+lagdx1))

x1.t<-ur.df(x1, type="trend", lags=1)
summary(x1.t)

x2.t<-ur.df(x2, type="trend", lags=1)
summary(x2.t)

# Cointegration Regression 

#cr<-lm(x2~x1)
cr<-lm(x2~tr+x1)
summary(cr)
res<-(cr$resid)

# Engle-Yoo Cointegration Test 

res1.t<-ur.df(res, type="drift", lags=1)
summary(res1.t)

res2.t<-ur.df(res, type="drift", lags=2)
summary(res2.t)

res3.t<-ur.df(res, type="drift", lags=3)
summary(res3.t)

res4.t<-ur.df(res, type="drift", lags=4)
summary(res4.t)

resaic.t<-ur.df(res, type="drift", selectlags=c("AIC"))
summary(resaic.t)

resbic.t<-ur.df(res, type="drift", selectlags=c("BIC"))
summary(resbic.t)