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A statistical hypothesis test assessing whether past values of one series improve prediction of another series.
DESCRIPTION
Granger causality tests whether lagged values of X contain information that helps predict Y beyond Y’s own history. It is implemented via nested regressions or VAR models and F-tests. The concept captures predictive causality, not necessarily true causal mechanisms. Stationarity and appropriate lag selection are critical. With cointegration, tests should use error-correction representations. Extensions exist for nonlinear and conditional Granger causality.
ALTERNATIVE DEFINITIONS
Wikipedia
A time series X is said to Granger-cause Y if past values of X provide statistically significant information about future values of Y.
Emphasizes predictive information over true causation.
Encyclopaedia Britannica
Granger causality is a statistical concept of causality that is based on prediction.
Concise emphasis that it concerns prediction-based causality.
statsmodels
The null hypothesis is that the time series in the second column does not Granger cause the time series in the first column.
Operational testing definition in software context.
RELATED TERMS
Vector Autoregression Causation Lag Variable Stationarity Cointegration Transfer Entropy Directed Acyclic Graph Time-lagged Dependence Forecasting Hypothesis Testing
COMPETING TERMS
Pearson Correlation Structural Causal Model
RELATIONS
- Broader: Causality
KNOWLEDGE AREAS
TARGET AUDIENCE
EXTERNAL SOURCES
- Wikipedia - Granger causality
- statsmodels - Python function for Granger tests
- Penn State STAT 501 - Course notes on VAR and Granger
TOP QUESTIONS
What does Granger Causality test?
It tests whether past values of one variable improve prediction of another. It is about predictability, not true causation.
Category: Definition
How is Granger Causality implemented?
Using nested regressions or VAR models and F-tests (or Wald tests) on lagged coefficients.
Category: HowTo
What assumptions underlie Granger Causality?
Stationarity, appropriate lag length, and absence of omitted confounders are key. Cointegration requires error-correction forms.
Category: Requirements
Can Granger Causality imply true causation?
No, it only implies predictive causality. Structural causal analysis is needed for causal claims.
Category: Misunderstanding
How to choose lag length for Granger tests?
Use information criteria (AIC/BIC), residual diagnostics, or domain knowledge.
Category: HowTo
What if variables are nonstationary?
Difference them or use a VECM if cointegrated to avoid spurious results.
Category: Practice
Are there nonlinear Granger tests?
Yes, there are kernel-based and other nonlinear extensions to capture nonlinear predictive relations.
Category: Topic
What’s a common mistake with Granger Causality?
Ignoring confounding variables can produce misleading results. Include relevant controls when feasible.
Category: Mistakes
Which tools support Granger testing?
statsmodels (Python), EViews, Stata, and R packages like vars and lmtest.
Category: Tooling