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Correlation between a time series and lagged versions of itself.
DESCRIPTION
Autocorrelation measures linear dependence of a series on its past values at different lags. The autocorrelation function (ACF) helps identify patterns, seasonalities, and model orders. Significant autocorrelation indicates memory in the process; white noise shows none beyond lag zero. Correlograms visualize ACF with confidence bands. Diagnostics like the Ljung–Box test assess residual independence after model fitting.
ALTERNATIVE DEFINITIONS
NIST Engineering Statistics Handbook
Autocorrelation is the correlation of a signal with a delayed copy of itself as a function of delay.
General signal-processing perspective emphasizing lagged self-correlation.
Penn State Eberly College of Science
Autocorrelation is the correlation between observations of a time series separated by k time units.
Time-series specific definition using lag-separation wording.
RELATED TERMS
Lag Partial Autocorrelation Stationarity Autoregressive Moving Average Correlogram Ljung–Box Test Spectral Density Temporal Data White Noise Autocorrelation Function
COMPETING TERMS
RELATIONS
- Broader: Correlation
- Narrower: Autocorrelation Function Partial Autocorrelation
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist Data Analyst AI Engineer
EXTERNAL SOURCES
- Wikipedia - Autocorrelation
- statsmodels - ACF function reference
- FPP3 (Hyndman & Athanasopoulos) - ACF interpretation guide
TOP QUESTIONS
How is Autocorrelation used in model selection?
Patterns in the ACF guide AR and MA order selection. For example, slow ACF decay suggests AR terms, while spikes at specific lags suggest MA or seasonal components.
Category: How-to
What does significant Autocorrelation in residuals indicate?
It signals model misspecification, omitted dynamics, or non-stationarity. Residuals should resemble white noise if the model captures structure well.
Category: Risks
How do seasonality and Autocorrelation relate?
Seasonal processes show ACF spikes at seasonal lags (e.g., 12 for monthly data). These features guide SARIMA or seasonal components.
Category: Concept
What is Partial Autocorrelation versus Autocorrelation?
PACF measures correlation at a given lag after removing effects of smaller lags. It is often used to identify AR order.
Category: Concept
How do I test for overall Autocorrelation?
Use portmanteau tests like Ljung–Box on residuals. Significant results indicate remaining serial correlation requiring model refinement.
Category: How-to
Can Autocorrelation be non-linear?
ACF measures linear dependence. Non-linear dependence may require alternative diagnostics, such as mutual information or non-linear tests.
Category: Concept
What are common mistakes when interpreting ACF plots?
Misreading random spikes within confidence bounds as structure, or ignoring seasonal lags. Always consider sample size effects and multiple comparisons.
Category: Mistakes
How does differencing affect Autocorrelation?
Differencing reduces low-lag autocorrelation by removing trend or seasonality. Over-differencing may induce negative autocorrelation and increase noise.
Category: Effects
Is Autocorrelation always undesirable?
No. In raw data, it reveals meaningful structure to model. In residuals, it’s undesirable because it indicates model inadequacy.
Category: Misunderstanding