1.16

n=1000
theta = 0.5
w = rnorm(n+1)
u = rnorm(n+1)
x = rep(0,n+1)
y = rep(0,n+1)
for (i in 2:(n+1)){
  x[i] = 0.98*x[i-1] + w[i]
  y[i] = 1 + w[i] + u[i] + theta*u[i-1] 
}

x=ts(x[-1])
y=ts(y[-1])
z = cbind(x,y)
plot(z)

acf( z,lag.max=20)