Question: 11.3 Suppose that a time series process {yt } is generated by yt z et , for all t 1,2,, where {et

11.3 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 se 2. The random variable z does not change over time; it has mean zero and variance sz 2. 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 ,yth) for any t and h. Is {yt } covariance stationary? (iii) Use parts (i) and (ii) to show that Corr(yt ,yth) sz 2/(sz 2 se 2) for all t and h.

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

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