Solved: Why use autocorrelation instead of autocovariance when examining stationary time series?

We can use the autocorrelation of the residuals from our estimated time-series model to assess model fit. The autocorrelation between one time-series observation and another one at distance k in time is known as the kth order autocorrelation.

     A correctly specified autoregressive model will have residual autocorrelations that do not differ significantly from zero

In order to determine whether a time series is an AR(p) or a MA(q), we can examine the autocorrelations. The autocorrelations for an AR model will generally begin as large values and gradually decline. The autocorrelations for a MA model will drop dramatically after q lags are reached, identifying both the MA process and its order.