Granger causation is a definition of causal relation between vectors in vector time series.
Let us define Ht as the history up to and including the discrete time t , and denote Yt the random vector Y at time t . Granger states that Yt causes Xt+1 if
| Pr(Xt+1 ÃŽ A | Ht) ¹ Pr(Xt+1 ÃŽ A | Ht – Yt) |
for some set A . Pr( a | b) here denotes conditional probability of a provided b . In common words, Granger says that Yt causes Xt+1 if the probability that Xt+1 belongs to a set A depends on whether Yt has taken place or not.