Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 6

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.

Step 1 of 6

Given that for all