1. Let {Xt} be the stationary process with mean of u and the ACVF y(h) and ACF p(h) = y(h)/y(0). The best linear predictor for predicting Xtth is of the form I(Xn) = Bo + BIXn such that lx(Xn) = arg min E[Xnth - 1(Xn)]2 = arg min E[Xnth - Bo - BIXn]. Show that best linear predictor is 1(Xn) = u(1 - p(h)) + p(h) Xn. (Hint) First, you have to utilize the fact that {Xt} is stationary, that is, 1. ux(t) is independent of t 2. y(h) = Cov(Xt, Xtth) is independent of t. Next, define L(Bo, B1) = E[Xnth - Bo - BIXn]2. and solve the optimization problem (BB, BY) = arg min L(Bo, B1). (Bo, B1) Then, show that lx (Xn) = BB + BIXn where Bo = M(1 - p(h)), Bo = p(h). (Hint for the above Hint) Recall how to derive the "LS" estimator in STA 4322