A 'weakly stationary' time series has the property that the autocorrelation is only dependent on the lag and its structure does not change over time apart from the properties of constant mean and constant finite variance. How does this imply that it's autocorrelation function (ACF) plots should show a decline to 0?
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1I don't think the claim is true as stated. Let $Z$ be standard normal and $X_t \equiv Z$ for all $t$. The series is stationary, but all the autocorrelations is 1 so does
– kjetil b halvorsen May 19 '21 at 15:13 -
1Thanks! I've since come to realize that it's more of a rule of thumb and not true always. It's explained in more depth in the link and its associated links: https://stats.stackexchange.com/questions/45502/acf-and-stationarity – Gomzy May 20 '21 at 05:56