set.seed(123)
time<-c(1:100)
time

y1<-w<-rnorm(100)
y1
w

for(t in 2:100) y1[t]=0.8*y1[t-1]+w[t]
y1
y1.ts<-ts(y1)

y2<-y1
for(t in 1:100) y2[t]=y1[t]+0.1*time[t]
y2
y2.ts<-ts(y2)
y2.ts
plot(y2.ts, lwd=1, type="l")

y3<-y2

y11<-y1
y11d<-data.frame(y11)
y11d

wd<-data.frame(w)
wd
wd[50,1]<-10
wd
wd.ts<-ts(wd)

for(t in 2:100) y11[t]=0.8*y11[t-1]+wd.ts[t]
y11
y11.ts<-ts(y11)

for(t in 1:100) y3[t]=y11[t]+0.1*time[t]
y3
y3.ts<-ts(y3)
y3.ts

plot(y2.ts, ylim=c(-2,16),lwd=2, main="Shock to Trend-Stationarity Process",type="l")
abline(lm(y2.ts~time),col="red")
lines(y3.ts, lwd=2, lty=6, col="blue")