Simulate the three ARIMA models of Exercise 1 with the command arima. sim and compare the theoretical ACFs with the sample ACFs.

Data From Exercise 1:

Compute the variance and the ACF (lag-1 to lag-4) of the following ARMA models with \(\operatorname{Var}\left(a_{t}\right)=1\) :

(a) \(z_{t}=0.7 z_{t-1}+a_{t}\);

(b) \(z_{t}=0.4 a_{t-1}+a_{t}\);

(c) \(z_{t}=0.7 z_{t-1}+\) \(0.4 a_{t-1}+a_{t}\).