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 σ2e. The random variable z does not change over time; it has mean zero and variance σ2e 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) σ2z/(σ2z + σ2e) for all t and h.
(iv) Does yt satisfy the intuitive requirement for being asymptotically uncorrelated?
Explain.
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