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ML Academy

Introduced on day 22

Partial autocorrelation function (PACF)

The correlation between a series and its lag k after removing the effect of the lags in between; it isolates the direct dependence at each lag.

In detail

The PACF at lag k is the coefficient on lag k in a regression of the series on its first k lags. For an AR(p) process it cuts off after p, which is why it is paired with the ACF (which cuts off for MA processes) when narrowing candidate orders. On short noisy series the pattern is blurred, so treat it as a hint.