Granger Causality

Granger Causality is a method to check causality (i.e. cause and effect relationship) between two variables in a time series. It is a statistical hypothesis test of whether one time series is useful in predicting the other. According to Granger causality, if a signal X₁ causes a signal X₂, then past values of X₁ should contain information that helps predict X₂ above and beyond the information contained in past values of X2 alone.

Granger causality relationship assumes that:

1. The cause happens prior to its effect.

2. The cause has unique information about the future values of its effect.

Given these two assumptions about causality, Granger proposed to test the following hypothesis for identification of a causal effect of X on Y:

P [Y(t+1) ∈ A | I (t) ]  ≠  P [Y(t+1) ∈ A | I_-X (t) ]

Where P refers to probability, A is an arbitrary non-empty set, I(t) and I_-X (t) respectively denote the information available as of the time in the entire universe, and that in the modified universe in which X is excluded. If the above hypothesis is accepted, we say that X Granger-causes Y.