(30 points) Suppose that the monthly log return of a security rt follows the model rt = 0.1 + 0.3rt-2 + At + 0.2at-2, where {at} is a Gaussian white noise series with mean zero and variance 0.05. (a) Compute the mean and variance of the return series. (6 points) (b) Compute the autocorrelations of the return series for all lags. (14 points) (c) Compute the 1-step- and all the multistep-ahead forecasts of the return at the forecast origin t = h. (10 points) (30 points) Suppose that the monthly log return of a security rt follows the model rt = 0.1 + 0.3rt-2 + At + 0.2at-2, where {at} is a Gaussian white noise series with mean zero and variance 0.05. (a) Compute the mean and variance of the return series. (6 points) (b) Compute the autocorrelations of the return series for all lags. (14 points) (c) Compute the 1-step- and all the multistep-ahead forecasts of the return at the forecast origin t = h. (10 points)