Granger Causality

The foundational axiom of Granger Causality: a cause must occur before its effect. A time series X is said to Granger-cause Y if past values of X contain statistically significant information that helps predict future values of Y, beyond the information contained in past values of Y alone. This is strictly a forecasting improvement concept, not a mechanistic proof of causation. The test assumes that the future cannot cause the past, making it inherently directional in time.

Granger Causality tests require the underlying time series to be covariance stationary—meaning the mean, variance, and autocorrelation structure do not change over time. Non-stationary data, such as series with trends or seasonality, can produce spurious regression results where two completely unrelated variables appear causally linked. Practitioners must apply differencing, detrending, or cointegration analysis before testing to avoid false positives.

The standard implementation uses an F-test on nested regression models to determine if lagged values of X jointly provide statistically significant predictive power. The procedure involves:

• Unrestricted model: Regresses Y on its own past values plus past values of X
• Restricted model: Regresses Y only on its own past values
• Null hypothesis: All coefficients on lagged X terms are zero A significant F-statistic leads to rejection of the null, indicating X Granger-causes Y.

The choice of lag order critically impacts test validity. Too few lags omit relevant historical information, while too many lags consume degrees of freedom and inflate standard errors. Selection methods include:

• Akaike Information Criterion (AIC): Balances model fit against complexity
• Bayesian Information Criterion (BIC): Imposes a stricter penalty for additional parameters
• Cross-correlation function analysis: Identifies significant lag relationships empirically

Granger Causality is not mutually exclusive. It is possible—and common in supply chain systems—for X to Granger-cause Y and Y to simultaneously Granger-cause X. This feedback relationship occurs when both time series contain predictive information about each other. For example, inventory levels may Granger-cause order quantities, while order quantities simultaneously Granger-cause future inventory levels, creating a dynamic, interdependent system.

The test is vulnerable to latent confounding. If an unobserved third variable Z drives both X and Y with different time lags, the test may falsely indicate Granger Causality between X and Y. This is the critical distinction from structural causal inference: Granger Causality measures incremental predictive utility, not true causal mechanism. In supply chain disruption analysis, failing to account for a common macroeconomic shock can create phantom causal links between unrelated operational metrics.