For a process $y_t,$ demonstrate that the optimal $($minimum mean square error$)$ forecast of $y_{T+s}$ is the expectation of $y_{T+s}$ conditional on information available at time $T$ i$.$e$.(T|).$ Using simple examples from time series processes such as $AR(1)$ and $MA(1),$ explore any relationships between the optimal forecast functions and the autocorrelation functions. Why do such relationships arise?