# What is partial autocorrelation

## Interpret the Partial Autocorrelation Function (PACF)

The partial autocorrelation function is a measure of the correlation between the observations of a time series (y_{t} and y_{t – k}) after correcting for the presence of all other terms with a lower lag (y_{t – 1}, y_{t – 2}, ..., y_{t-k-1}).

### interpretation

Use the partial autocorrelation function in conjunction with the autocorrelation function to determine ARIMA models. Look for the following patterns in the partial autocorrelation function. Examine the peaks at each lag to see if they are significant. A significant spike extends beyond the limits of significance, suggesting that the correlation for this lag is non-zero.

template | importance | example |
---|---|---|

Large peak at lag 1, which decreases after a few lags. | A moving average term in the data. Find the order of the moving average term using the autocorrelation function. | |

Big spike at lag 1, followed by a dampened wave that alternates between positive and negative correlations. | A higher order moving average term in the data. Find the order of the moving average term using the autocorrelation function. | |

Significant correlations at lag 1 or 2, followed by insignificant correlations. | An autoregressive term in the data. The number of significant correlations indicates the order of the autoregressive term. |

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