Compute the ACF of the process (z_{t}=y_{t}+v_{t}), where (y_{t}=0.4 a_{t-1}+a_{t}) with (operatorname{Var}left(a_{t} ight)=4) and (v_{t}) a white

Compute the ACF of the process \(z_{t}=y_{t}+v_{t}\), where \(y_{t}=0.4 a_{t-1}+a_{t}\) with \(\operatorname{Var}\left(a_{t}\right)=4\) and \(v_{t}\) a white noise process with \(\operatorname{Var}\left(v_{t}\right)=2.0\) Simulate the series with the command arima.sim and compare the theoretical ACFs with the sample ACFs (first four lags).