The Granger (1969) approach to the question of whether
causes
is to see how much of the current
can be explained by past values of
and then to see whether adding lagged values of
can improve the explanation.
is said to be Granger-caused by
if
helps in the prediction of
, or equivalently if the coefficients on the lagged
’s are statistically significant. Note that two-way causation is frequently the case;
Granger causes
and
Granger causes
.