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When we run a AR model, we are using a linear combination of its lags to predict the current value. So this means that the lags are related to each other (at least t-1, t-2, ..., t-n are related to t0). On the other hand, stationarity is about independence. I can't understand why is that, what is happening. Can someone throw some light on this matter for me?

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    $\begingroup$ Stationarity is not about independence. Stationarity says the joint distributions of any section of the time series are the same as any other section, but that joint distribution can include any sort of dependence between observations $\endgroup$ Apr 3 at 2:08

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If you discombobulated the concepts of stationarity and independence, you should note that a sequence of random variables can be $m$–dependent as well as stationary. Stationarity only says you don't need to bother when you start counting when you are calculating the joint distribution of $(Y_k, \ldots, Y_{k+\ell}) $ as the latter won't depend on $k.$

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