(1) Obtain the variance of the k-step-ahead prediction error εn+k|n for an MA model of order 1; yn = vn −bvn−1, vn ∼ N(0,1). (2) Express an AR model of order 1, yn = ayn−1 +vn, using an MA model of...

(1) Obtain the variance of the k-step-ahead prediction error εn+k|n for an MA model of order 1; yn = vn −bvn−1, vn ∼ N(0,1).

(2) Express an AR model of order 1, yn = ayn−1 +vn, using an MA model of infinite order and obtain the variance of the k-step-ahead prediction error variance.

(3) Using the formal expansion of the random walk model yn = yn−1 + vn, obtain the MA model of infinite order. Using that expression, obtain the k-step-ahead prediction error variance of the random walk model.