set.seed(123)
x1<-w1<-rnorm(500)
for(t in 2:500) x1[t]=x1[t-1]+w1[t]
(x1.ts<-ts(x1))

set.seed(1234)
y1<-z1<-rnorm(500)
for(t in 2:500) y1[t]=y1[t-1]+z1[t]
y1.ts<-ts(y1)

par(mfrow=c(2,1))

plot(x1.ts)
plot(y1.ts)

lm(y1~x1)
ols1<-lm(y1~x1)
summary(ols1)

set.seed(123345)
x2<-w2<-rnorm(500)
for(t in 2:500) x2[t]=0.8*x2[t-1]+w2[t]
(x2.ts<-ts(x2))

set.seed(123456)
y2<-z2<-rnorm(500)
for(t in 2:500) y2[t]=0.5*y2[t-1]+z2[t]
y2.ts<-ts(y2)

plot(x2.ts)
plot(y2.ts)

lm(y2~x2)
ols2<-lm(y2~x2)
summary(ols2)