Covariance stationary clarification

From Kaplan:


So to qualify as covariance stationary, X sub t-2 = X sub t+2, and also X sub t = X sub t-1?

The forecast equals the lag?

Anyone, respectfully?

I think the key thing to note here is that the “distance” between any observations has to be the same on both the left and right hand sides of the covariance equations, which you see for option b). For a), you only have 1 observation period on the left hand side, but you have 2 on the right hand side.

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Perfect explanation; the “distance” between any observation has to be the same on both the left and right hand sides of the covariance equations. Excellent.