Write the equation for forecasting

Suppose that yt follows the model yt = a + dzt-1 + ut ut = ?ut-1 + et Et [et+1] = 0.

(a) Show that Et [yt+1] = (1 – ?)a + ?yt + d1zt – ?dzt-1.

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(b) Suppose that you use T observations to estimate a, d1 and ?.

Write the equation for forecasting yT +1.

(c) Explain why the model with one lag of z and AR(1) serial correlation is a special case of the model yt = a0 + ?yt-1 + ?1zt-1 + ?2zt-2 + et .

(d) What does part (c) suggest about using models with AR(1) serial correlation for forecasting?

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