I am asking myself how cointegration and causality are related in a VAR/VECM model.
Suppose you have two $I(1)$ variables in your 2 dim VAR process which are cointegrated, so there is one cointegration relationship.
In my opinion this should imply that the two variables are granger causal to each other?!
But, does this also imply that there is instantaneous causality between the two variables?
And the other way round:
Two $I(1)$ variables which are granger and (or) instantaneous causal. Does this imply, that they are also cointegrated?
Thanks a lot.
Best Answer
When two variables are cointegrated then it suggests that there should be Granger causality in at least one direction (X causes Y or Y causes X or both).
Granger causality doesn't give instantaneous causality. X is said to Granger cause Y if lagged values of X is helpful in predicting Y above and beyond the information contained in lagged values of Y alone.
Not necessarily.