The partial autocorrelation function is a measure of the correlation between observations of a time series that are separated by k time units (y_{t} and y_{t–k}), after adjusting for the presence of all the other terms of shorter lag (y_{t–1}, y_{t–2}, ..., y_{t–k–1}).

Use the partial autocorrelation and autocorrelation functions together to identify ARIMA models. Look for the following patterns on the partial autocorrelation function. Examine the spikes at each lag to determine whether they are significance. A significant spike will extend beyond the significant limits, which indicates that the correlation for that lag doesn't equal zero.

Pattern | Indicates | Example |
---|---|---|

Large spike at lag 1 that decreases after a few lags. | A moving average term in the data. Use the autocorrelation function to determine the order of the moving average term. | |

Large spike at lag 1 followed by a damped wave that alternates between positive and negative correlations. | A higher order moving average term in the data. Use the autocorrelation function to determine the order of the moving average term. | |

Significant correlations at the first or second lag, followed by correlations that are not significant. | An autoregressive term in the data. The number of significant correlations indicate the order of the autoregressive term. |