Granger Causation:

Granger causation is a definition of causal relation between vectors in vector time series .

Let us define H_t as the history up to and including the discrete time t , and denote Y_t the random vector Y at time t . Granger states that Y_t causes X_t+1 if

for some set A . Pr( a | b) here denotes conditional probability of a provided b . In common words, Granger says that Y_t causes X_t+1 if the probability that X_t+1 belongs to a set A depends on whether Y_t has taken place or not.

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