18.8 Suppose that PRO y = a +82-1+ u u = pu-1+e, REVIEW ONLYws the model E(e,1,-1) = 0, contains y and z dated at t -1 and earlier. - Show that E(y+1) = (1 - p)a + py, +8z, p8z. (Hint: Write u-1-1a-8-2 and plug this into the second equation; then, plug the result into the first equation and take the conditional expecta- tion.) (ii) Suppose that you use n observations to estimate

a, d, 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 y = do + py-1 + 12-1 + 1221-2 +

e. (iv) What does part (iii) suggest about using models with AR(1) serial cor- relation for forecasting?