Granger Causality: Forecasting, Not Causing

The mental model

Granger Causality does not prove that X causes Y. Instead, it's a statistical test to see if the past values of time series X are useful for forecasting the future values of time series Y. If knowing X's history improves your prediction of Y, then X is said to "Granger-cause" Y. Think of it as a test for predictive power, not a philosophical proof of causation.

How it works

The test compares two statistical models. The first model attempts to predict a time series (Y) using only its own past values (its autoregressive history). The second model predicts Y using both its own past values AND the past values of another time series (X). If the second model, which includes X's history, is statistically significantly better at predicting Y than the first model, we conclude that X Granger-causes Y. The key is whether adding X reduces the forecasting error for Y.

When to use it

Use this test when you have two or more time series and want to understand their predictive relationships. It is a common tool in econometrics for exploring links between variables like GDP and employment. In system observability, you could test if historical error rates in a microservice are useful for forecasting latency spikes in a downstream dependency.

When not to use it

Do not use this test to claim true causality. This is the biggest and most common mistake. The test only reveals precedence and predictive ability, falling victim to the "post hoc ergo propter hoc" fallacy (after this, therefore because of this). It also cannot account for confounding variables; a hidden third factor, Z, could be driving both X and Y, creating a spurious relationship. It is a starting point for analysis, not the conclusion.

One canonical example

An economist wants to know if changes in a country's money supply help predict future inflation. They gather time series data for both. A Granger causality test reveals that past values of the money supply significantly improve the forecast for future inflation, even after accounting for inflation's own history. The correct conclusion is not "increasing the money supply causes inflation," but that "money supply Granger-causes inflation," meaning it is a statistically useful leading indicator.