Question: Let Xt be defined such that Let {X} be defined such that, for {Zt} ~ WN(0, o2) (where WN(u, 02) indicates a white noise process

Let Xt be defined such that

Let {X} be defined such that, for {Zt} ~ WN(0, o2) (where WN(u, 02) indicates a white noise process with mean 0 and variance o2), we have Xt = Z+ + 02Zt-2. (a) [12 marks] Find the autocovariance function yx (h) for lags h = {0, 1, 2, 3}. (b) [5 marks] Find the best linear predictor of Xt given Xt-1 and Xt-2. (c) [5 marks] Find the best linear predictor of Xt given Xt+1 and Xt-1. (d) [3 marks] Find the mean-squared error of prediction for the answer in part (c)

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