Suppose
Suppose A and B are random variables that are independent of Xt.
What are the steps to check whether {Yt} is covariance stationary?
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2Apply the definition. Presumably you have tried that. What is your definition and where do you get stuck? – whuber Oct 04 '22 at 17:45
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@whuber I get stuck when finding the Cov(Yt, Yt+h) – Geek_Tech Oct 05 '22 at 04:08
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@whuber I would like to know the expected value of (B, εt). Are B and εt independent? – Geek_Tech Oct 05 '22 at 05:15
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2You need to interpret "Suppose A and B are random variables that are independent of Xt" as applying to all $t\in\mathbb Z.$ Thus, for any $t,$ $B$ is independent of $X_t$ and $X_{t-1},$ which implies it is independent of $X_t - X_{t-1} = \varepsilon_t.$ – whuber Oct 05 '22 at 13:50
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@whuber thanks for the great explanation. I could observe that Yt is not covariance stationary but the first difference of Yt is covariance stationary. Hope I am correct. – Geek_Tech Oct 05 '22 at 16:58
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1That sounds correct to me. There's much to be learned from a rigorous demonstration, though. In particular, you don't have to assume $A$ and $B$ are independent. – whuber Oct 05 '22 at 17:31