 Partial autocorrelation function

The partial autocorrelation at lag $k$ is the correlation of $X_t$ and $X_{t-k}$ after their linear projections onto the intervening observations are removed. A causal autoregressive model of order $p$ has zero partial correlations after lag $p$. This complements the finite cutoff of the autocorrelation function for a moving-average model.

The Partial Autocorrelation Function (PACF) is a statistical tool used in time series analysis to measure the degree of association between a time series and its own lagged values, while controlling for the effects of intervening lags. It helps to identify the direct relationship between the current value of the series and its past values, excluding the influence of other lags.