📊Partial Autocorrelation

NEW

Also known as: PACF

Correlation between a series and its lagged values after removing the linear effects of intervening lags.

DESCRIPTION

Partial autocorrelation quantifies the direct relationship between a time series and its lag-k version, controlling for lags 1 to k−1. It is central to identifying autoregressive (AR) order: a PACF that cuts off after lag p suggests AR(p). Estimation methods include Yule–Walker and Durbin–Levinson recursions. Confidence intervals help assess significant lags under stationarity assumptions. PACF complements the ACF when applying Box–Jenkins methodology.

ALTERNATIVE DEFINITIONS

NIST/SEMATECH e-Handbook of Statistical Methods

The partial autocorrelation at lag k is the correlation between X_t and X_{t−k} with the linear dependence of the intermediate lags 1 through k−1 removed.

Emphasizes control for intermediate lags in defining partial correlation.

Source

statsmodels

The partial autocorrelation function (PACF) gives the partial correlation of a stationary time series and its lagged values.

Library reference linking PACF to stationarity and implementation details.

Source

RELATED TERMS

ARIMA Yule-Walker Equations Durbin–Levinson Algorithm Box–Jenkins Stationarity Temporal Data Lag Model Order Selection

COMPETING TERMS

Autocorrelation Function

RELATIONS

• Broader: Autocorrelation

KNOWLEDGE AREAS

Data Science Mathematics AI

TARGET AUDIENCE

Data Scientist MLOps Engineer AI Engineer Data Analyst

EXTERNAL SOURCES

• Wikipedia - Partial autocorrelation function
• Penn State STAT 510 - Course notes on ACF and PACF.
• Forecasting: Principles and Practice - Applied PACF guidance for ARIMA.

TOP QUESTIONS

How does Partial Autocorrelation help in AR model selection?

A PACF that cuts off after lag p suggests an AR(p) order, aiding Box–Jenkins identification.

Category: How-To

What is the difference between PACF and ACF?

PACF measures direct lag relationships after controlling for shorter lags; ACF measures overall correlation including indirect effects.

Category: Concepts

Can PACF be used on non-stationary series?

It should be applied to stationary data. Difference or transform the series before interpreting PACF.

Category: Requirements

How do I interpret PACF confidence bands?

Spikes outside bands indicate significant partial correlation at that lag under approximate white noise assumptions.

Category: Interpretation

Which estimator for PACF should I use?

Yule–Walker and Durbin–Levinson are common; software defaults are usually adequate for exploratory purposes.

Category: Guidance

What is a common mistake with PACF?

Overinterpreting small spikes without considering sampling variability and multiple comparisons.

Category: Mistakes

How many lags should I plot in PACF?

Plot enough lags to cover plausible AR orders, often up to 20–40 depending on data frequency and domain knowledge.

Category: Best practices

Does seasonality affect PACF?

Yes. Seasonal spikes appear at multiples of the seasonal period in seasonal AR models.

Category: Concepts

Is PACF useful for MA models?

PACF tails off for pure MA processes; ACF cutoff is the primary indicator for MA order.

Category: Concepts