Overview
Granger causality is a definition of causality proposed by Clive Granger in the study of economic data. Granger proposed that a time series {% X_t %} can be said to be causal to another time series {% Y_t %} if information about current and past values of {% X_t %} is useful in predicting value of {% Y_t %}.
Within an information theory perspective, one could assert that the mutual information of causally related variables is greater than zero.
Granger Test
The test that Granger proposed made some assumptions.
- Both time series are covariance stationary
- The optimal forecast is linear
{% Y_t = \alpha + \beta_1 X_{t-1} + \beta_2 X_{t-2} + ... + \beta_n X_{t-n} %}
The test Granger proposed was the standard
F-Test.
That is, the F test tests the hypothesis that not all the {% \beta %}'s given above are zero.