Suppose that yt follows the model yt = + 1 zt-1 + ut u, = put-1 + et E(et | It-1) = 0, where

Suppose that yt follows the model
yt = α + δ1 zt-1 + ut
u, = put-1 + et
E(et | It-1) = 0,
where It-1 contains y and z dated at t - 1 and earlier.
(i) Show that E(yt+1| It) = (1 - p) α + pyt + δt Zt - p δl Zt-1
(ii) Suppose that you use n observations to estimate α, δ1, and p. Write the equation for forecasting yn+1.
(iii) Explain why the model with one lag of z and AR(1) serial correlation is a special case of the model
yt = α0+ pyt-1 + γ1 zt-1 + γ2 zt-2 + et.
(iv) What does part (iii) suggest about using models with AR(1) serial correlation for forecasting?