seniorTime Series
What is Partial Autocorrelation Function (PACF) and how is it different from ACF?
Updated May 15, 2026
Short answer
PACF measures direct correlation between a time series and its lag, removing effects of intermediate lags.
Deep explanation
PACF isolates the direct effect of a lag by removing indirect influences from shorter lags. While ACF includes both direct and indirect correlations, PACF shows only the pure relationship at each lag. This makes PACF essential for determining AR(p) order in ARIMA models.
Real-world example
Identifying direct influence of yesterday’s sales on today’s sales excluding intermediate days.
Common mistakes
- Interpreting PACF as simple correlation instead of partial correlation.
Follow-up questions
- Why is PACF used for AR order selection?
- How do ACF and PACF complement each other?