# Granger causality and cointegration

I have two time series, which are both I(1). I run an ADLM(4) model and compared it with a DLM(4) model (unidirectional: Does X granger causes y?), but the statistic was not significant. Therefore, X does not have any incremental predicting power of Y. I can conclude that X does not granger caused Y.

QUESTION:

1. Is it meaningful to test for cointegration, knowing there is no granger causality?
2. What is the link between granger causality and cointegration?
• @RichardHardy, of course. I got confused in my code. I have edited the question. Commented Dec 7, 2017 at 12:16
• @RichardHardy, thanks for your help, the answer makes it perfectly clear! Commented Dec 7, 2017 at 13:38

• Can you elaborate on "Cointegration between a pair of time series implies presence of Granger causality"? Take $X_t = t + e_t$ and $Y_t = -X_t = -t - e_t$. I would say X and Y are cointegrated (as $X+Y=0$) but neither Granger causes the other, as lagged values of one does not improve prediction of the other. Commented Oct 23, 2022 at 17:30