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The definition for the $k$-th lag auto correlation is $Cov(y_t,y_{t-k})/Var(y_t)$.
My question is why should not it be $Cov(y_t,y_{t-k})/[Var(y_t)\cdot Var(y_{t-k})]^{0.5}$.
In another words, what is it different from the correlation coefficient between $y_t$ and $y_{t-k}$?

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I guessed the question, since you probably hit post too soon. See if it is ok. – mpiktas Jun 20 '11 at 6:48

Auto-correlation is defined for stationary processes. The stationary process has constant mean and constant variance, hence $Var(y_t)=Var(y_{t-k})$ for all $t$ and $k$. With this in mind the definitions coincide.

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