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I did not write the limit in my notes but it must be there otherwise this equality has no chance of being true under mild conditions.
Monolite
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Property of the autocovariance function in time series

In the framework of time series analysis

Why does $\lim_{n \rightarrow \infty} n^{-1} \sum_{|h| <n} |\gamma(h)| = \lim_{n \rightarrow \infty} 2|\gamma(n)| $?

Adding some steps in-between might help me greatly.

Where $\gamma(h)$ is the auto-covariance function defines as $\gamma(h) \equiv Cov(X_{t+h}, X_t)$.

Monolite
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