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Can the idiosyncratic error term of a variable Y increase without the covariance of Y and X increasing?
If an outcome, variable $Y$, consists of a noise or idiosyncratic error ($e$) that is orthogonal to an independent variable, $X$, is it possible to increase $e$ without changing the $Cov(Y,X)$?
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Zero conditional expectation implying zero covariance?
Proof: E[X|Y]=0 implies COV[X,Y]=0
I was thinking maybe the law of total covariance or tower rule but couldn't come up with the proof
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Can someone explain me how I compute $Cov[X_t, X_{t+1}]$ in this case?
I have some problems computing the autocovariance in the above exercise.
Especially when given different lags, I do not understand why the number of lags is in the exponent of $\phi$.
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