Suppose that the simple return of a monthly bond index follows the MA(1) model

\[ R_{t}=a_{t}+0.2 a_{t-1}, \quad \sigma_{a}=0.025 \]

Assume that \(a_{100}=0.01\). Compute the 1 -step- and 2 -step-ahead forecasts of the return at the forecast origin \(t=100\). What are the standard deviations of the associated forecast errors? Also compute the lag-1 and lag-2 autocorrelations of the return series.