Granger Causation

Granger Causation:

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 ÃƒÅ½ A | Ht) Ã‚Â¹ Pr(Xt+1 ÃƒÅ½ 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.

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