Consider the MA(1) series X = w, +0w,-1, where w, is white noise with variance o. (a) Derive the minimum mean-square error one-step forecast based on the infinite past, and determine the mean-square error of this forecast. (b) Lett be the truncated one-step-ahead forecast as given in (3.92). Show that E [(Xn+1 - Ft)?] = oʻ(1 + 02+2n). Compare the result with (a), and indicate how well the finite approximation works in this case. are Property 3.7 Truncated Prediction for ARMA For ARMA(p, q) models, the truncated predictors for m = 1, 2, ..., a + ... +0 (3.92) where xi" = x; for I si s n and 8" = 0 for 1 s 0. The truncated prediction errors are given by: w" = 0 for 1 s 0 or 1 > n, and w = $(B)X"-0,6 -0,4 for 1 sisn.