Suppose that Yt follows the stationary AR(1) model Yt = 2.5 + 0.7Yt - 1 + ut,
where ut is i.i.d. with E(ut) = 0 and var1ut2 = 9.
a. Compute the mean and variance of Yt.
b. Compute the first two autocovariances of Yt.
c. Compute the first two autocorrelations of Yt.
d. Suppose that YT = 102.3. Compute YT+1|T = E(YT+1 |YT, Yt - 1, . . . . ).