Consider the ARMA(1,1) model described by yt = 095yt 1 +08 t 1+ t with t N(01) for all t

(a) Show that the one-step-ahead truncated forecast is given by yt t+1 =

095yt + 08 t t

with t t

computed recursively via t j

095yj 1 08 t j 1 , for j = 1 : t with t 0 = 0 and y0 = 0.

(b) Show that the approximate mean square prediction error is MSEt t+h = v 1+ ( + )2(1 2(h 1))

(1 2)

= yj