Suppose that a time series process 5yt 6 is generated by yt 5 z 1 et

, for all t 5 1, 2, p, where 5et 6 is an i.i.d. sequence with mean zero and variance s2

e. The random variable z does not change over time; it has mean zero and variance s2 z. Assume that each et is uncorrelated with z.

(i) Find the expected value and variance of yt

. Do your answers depend on t?

(ii) Find Cov1yt

, yt1h 2 for any t and h. Is 5yt 6 covariance stationary?

(iii) Use parts (i) and (ii) to show that Corr1yt

, yt1h 2 5 s2 z/1s2 z 1 s2 e 2 for all t and h.

(iv) Does yt satisfy the intuitive requirement for being asymptotically uncorrelated? Explain.