**Unformatted text preview: **Y t-1 , Y t-2 , . . . . Let f t-1 denote some forecast for Y t that is based on Y t-1 , Y t-2 , . . . . We judge the quality of the forecast by the conditional mean squared forecast error E[( Y t-f t-1 ) 2 | Y t-1 , Y t-2 , . . . ]. Show that taking f t-1 = E[ Y t | Y t-1 , Y t-2 , . . . ] mini-mizes the conditional mean squared forecast error. 3. Consider the AR(p) model under the assumption E[ u t | Y t-1 , . . . , Y t-p ] = 0. Show that this assumption implies that Cov[ u t , u t-j ] = 0 for all j 6 = 0. 1 Problem 3 Consider the stationary AR(1) model Y t = 2 . 7 + 0 . 7 Y t-1 + u t , where u t is iid with E[ u t ] = 0 and variance Var[ u t ] = 9. 1. Compute the mean and variance of Y t . 2. Compute the first two autocovariances of Y t . 3. Compute the first two autocorrelations of Y t . 4. Suppose Y T = 102 . 3.Compute Y T +1 | T = E[ Y T +1 | Y T , Y t-1 , . . . ]. 2...

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- Fall '18