try evaluating both of the covariances at lag 1 and you will almost certainly find that one of them is 0 and one of them isn't. Try to understand why.My question is: am I right to assume both and are 0 at any lag h?

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Looking at that series i expect it is stationary but i dont know how to prove it without doing the whole question for you. Have a go if you like and post if you get stuck.