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1. Consider an ARMA(1,1) process yt = Bo+ pyt-1+ Et + 01Et-1, (1) for t = 1, 2, . . . , T, where at ~ WN (0, 02). The lag polynomials 1 - 41 = 0 and 1 + 01 1 = 0 have roots that are greater than 1 in absolute value (their inverse roots are less than 1). Note that the information set is given by 321 = {yt, yt-1, yt-2, " "' , Et, Et-1, Et-2, . ..). (a) Compute yrth,7 using estimates Bo, 9, 01 for h = 1, 2,3. You need to write your fore- casts in terms of the parameters in the true model, your estimated parameters, (1) and elements of 2t. (b) Compute erth,T for h = 1, 2, 3. (c) Compute of = var (erth,r) for h = 1, 2 (write it in terms of the parameters in (1))