# Population autocovariance goes to zero, assuming covariance stationary

by Vivian Miller   Last Updated October 14, 2018 16:19 PM

In time series context, let $$\gamma_j=E[(y_t-\mu)(y_{t-j}-\mu)]$$ denote population autocovariance, where $$\mu$$ is population mean of $$y_t$$, assuming covariance-stationary. Then, $$\gamma_j$$ goes to $$0$$ as $$j$$ goes to $$\infty$$.

I have been trying to use algebra to prove $$\gamma_j$$ goes to $$0$$ for a while, but cannot figure it out. Could anyone give me a hint on how to understand this limiting behavior?

Tags :