# Granger causality in time series

Granger causality uses the notion of VAR models where we can create two models one using the prediction of X alone and another using X and Y. If X,Y model performs better we can say that X causes Y. At many web resources, there is a mention of F-score and p-value to determine Granger causality. Where do they fit in with VAR models for determining Granger causality

• "we can say that X Granger- causes Y." – Firebug Feb 8 '17 at 18:13

I am not sure if I understand your question... Consider a VAR model for ($x,y$). You test joint zero restrictions on all lags of $x$ in the equation of $y$ to find whether $x$ Granger-causes $y$. The test is an $F$-test, and the test statistic has an associated $p$-value. If the $p$-value is low enough, you reject the null hypothesis of noncausality in favour of causality. Is anything missing here?
• You set the coefficients on lags of $x$ to zero -- that is what I mean by zero restrictions. – Richard Hardy Feb 9 '17 at 19:54