Consider the following stationary process xt = _ yt􀀀1 + yt; yt = (_ + _ y2 t􀀀1)1=2 zt; with j_j 1, _ > 0, 0 _ _ 1 and fztg is an i.i.d. N(0; 1) sequence. (a) Determine the autocovariance function of...

Consider the following stationary process

xt = _ yt􀀀1 + yt;

yt = (_ + _ y2 t􀀀1)1=2 zt;

with j_j 1, _ > 0, 0 _ _ 1 and fztg is an i.i.d. N(0; 1) sequence.

(a) Determine the autocovariance function of fytg.

(b) Determine the autocovariance function of fxtg.

Hint: Recall that if X and Y are random variables, then E[g(X)] = E fE [g(X) j Y ]g.