Partial Autocorrelation
The correlation between a time series and its lagged version, controlling for the effects of all intermediate lags.
What is Partial Autocorrelation?
While standard autocorrelation measures the relationship between a current value and a past value including all indirect effects through intervening periods, partial autocorrelation (PACF) isolates the direct effect. For example, the partial autocorrelation at lag 3 removes the variance explained by lags 1 and 2.
Why Partial Autocorrelation Matters
It is a crucial diagnostic tool in time series analysis (Box-Jenkins methodology) used specifically to identify the correct number of autoregressive (AR) terms to include in an ARIMA model.
Example
A forecaster looking at monthly retail sales uses a PACF plot. Seeing a significant spike at lag 1 and lag 2, but nothing afterward, they decide an AR(2) model is appropriate.
Common Mistakes
- Confusing PACF with standard ACF when trying to identify Moving Average (MA) processes.
- Over-interpreting marginal spikes in the PACF plot that fall just on the edge of the confidence intervals.