Suppose that the daily log return of a security follows the model rt = 0.01 + 0.2rt−2 + at, where {at} is a Gaussian white noise series with mean zero and variance 0.02.

What are the mean and variance of the return series rt? Compute the lag-1 and lag-2 autocorrelations of rt. Assume that r100 =−0.01, and r99 = 0.02.

Compute the 1-step 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?