3.11 Consider the MA(1) seriesxt = wt θ wt-1,where wt is white noise with variance ^2.(a) Derive the minimum mean-square error one-step forecast based on the infinitepast, and determine the mean-square error of this forecast.(b) Let xn 1^n be the truncated one-step-ahead forecast as given in (3.92). Show thatE[(xn 1 - xn 1^n)^2] = σ^2(1 θ^2 2n).Compare the result with (a), and indicate how well the finite approximation worksin this case.
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