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.