When your autocorrelation becomes negative

The negative values appearing at larger lags in the sample autocorrelation function are usually not evidence of true negative dependence but arise from the finite-sample constraint that the estimated autocorrelations must balance around zero once the sample mean has been removed.

Positive autocorrelation at small lags forces the estimated ACF at larger lags to become slightly negative because the correlations must balance around zero in a finite sample.

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