Introduction to Econometrics 3rd Edition by James Stock, James Stock

تمرين 5

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