Suppose that the daily \(\log\) return of a security follows the model

\[ r_{t}=0.01+0.2 r_{t-2}+a_{t} \]

where \(\left\{a_{t}\right\}\) is a Gaussian white noise series with mean zero and variance 0.02 . What are the mean and variance of the return series \(r_{t}\) ? Compute the lag- 1 and lag-2 autocorrelations of \(r_{t}\). Assume that \(r_{100}=-0.01\), and \(r_{99}=0.02\). Compute the 1- and 2-step-ahead forecasts of the return series at the forecast origin \(t=100\). What are the associated standard deviations of the forecast errors?