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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?
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  • $\begingroup$ @RichardHardy, of course. I got confused in my code. I have edited the question. $\endgroup$ – user1607 Dec 7 '17 at 12:16
  • $\begingroup$ @RichardHardy, thanks for your help, the answer makes it perfectly clear! $\endgroup$ – user1607 Dec 7 '17 at 13:38
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The null hypothesis of the Granger causality test is that there is no Granger causality. Hence, your result tells you there is not enough data to conclude otherwise.

Answer to Question 2: Cointegration between a pair of time series implies presence of Granger causality at least one way. That is, at least one of two series Granger-causes the other one. Intuitively, the series must be "related" (specifically, in the sense of Granger-causality) to be cointegrated.

Answer to Question 1: In theory, if there is no Granger causality, you already know there will be no cointegration. In practice, tests may have limited power, and models used for testing may not be adequate for the time series at hand. Hence, sometimes you may find contradictory results, e.g. that there is cointegration but there is no Granger-causality. On such occasions it is best to inspect the possible causes of this contradiction (check whether the models are adequate for the data).

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