Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 14

Suppose that a time series process {yt} is generated by yt = z _ et, for all t = 1, 2, …, where {et} is an i.i.d. sequence with mean zero and variance 2e. The random variable z does not change over time; it has mean zero and variance 2e 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 Cov(yt, yt+h) for any t and h. Is {yt} covariance stationary
(iii) Use parts (i) and (ii) to show that Corr(yt, yt+h) 2z/( 2z + 2e) for all t and h.
(iv) Does yt satisfy the intuitive requirement for being asymptotically uncorrelated
Explain.