Granger Causality

Traders often wonder whether one market leads another: does oil predict airline stocks, do futures lead the cash market, does one crypto exchange move before others? Granger causality, named after economist Clive Granger, gives a statistical way to test this. A series X is said to "Granger cause" Y if past values of X help predict Y better than past values of Y alone. Despite its name, it measures predictive usefulness, not true cause and effect.

The idea#

Compare two models for predicting Y:

restricted: Y_t = a + Σ b_i × Y_(t-i) + e_t
unrestricted: Y_t = a + Σ b_i × Y_(t-i) + Σ c_j × X_(t-j) + e_t

If adding past values of X significantly improves the prediction (tested with an F test on the c coefficients), X Granger causes Y.

Steps to run the test#

1. Make both series stationary, usually by using returns or differences. See Stationarity, Differencing and Unit Roots.
2. Choose the number of lags, often with information criteria such as AIC or BIC.
3. Estimate both models and run the F test.
4. Test both directions: X to Y and Y to X. Feedback in both directions is possible.

Market examples#

Granger causality is not true causality#

Relation to vector autoregressions#

Granger causality is often tested inside a vector autoregression (VAR), a model in which several series are each explained by their own and each other's past values. VARs are widely used in macroeconomics to study how interest rates, inflation and output affect each other. See Econometrics.

How traders use it#

• Finding lead lag signals across related markets.
• Choosing hedging instruments that move first.
• Understanding price discovery: which venue sets the price. See Price Discovery.
• Building features for models. See Feature Engineering.

Always confirm that any predictive link survives costs, out of sample testing and realistic execution delays.

Frequently asked questions#

What is Granger causality?#

A statistical test of whether past values of one time series improve predictions of another beyond what the second series' own past provides.

Does Granger causality prove causation?#

No. It shows predictive usefulness; a third factor or timing differences can create Granger causality without true cause and effect.

How is Granger causality used in trading?#

To find lead lag relationships between markets, such as futures leading cash markets, and to build predictive features.

Next, learn how to calculate statistics over moving periods in Rolling and Expanding Windows.