What is the difference in terms of inference? Does Instantaneous captures the short term cause and effects?
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$\begingroup$ Some related threads can be found here, though perhaps they are of limited relevance. $\endgroup$– Richard HardyCommented Apr 20, 2019 at 17:08
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$\begingroup$ Thanks @RichardHardy. I have another question if u could help regarding the use of VAR with 2 variables being I0 and 2 I1, with the latter having cointegration. Can i still use VAR for short term analysis and Granger Causality? $\endgroup$– Constantinos RousosCommented Apr 20, 2019 at 17:14
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$\begingroup$ There are a number of similar questions on this site, try searching for them. I personally have answered a couple, I think. If you fail to find them, let me know. $\endgroup$– Richard HardyCommented Apr 20, 2019 at 17:18
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$\begingroup$ @RichardHardy believe me I’ve read all of them😕. The problem is that I don’t know how to ‘mix’ the cointegrated vector with the two stationary variables, in terms of R coding, or worse if I can create such an equation? $\endgroup$– Constantinos RousosCommented Apr 20, 2019 at 17:31
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$\begingroup$ R coding happens to be off topic here, while the question of whether you can create such an equation is addressed in the posts I mentioned, is it not? $\endgroup$– Richard HardyCommented Apr 20, 2019 at 18:12
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I was looking for the answer to this same question and I found it on the book Introduction to Modern Time Series Analysis (second edition) by Gebhard Kirchgassner, Jurgen Wolters and Uwe Hassler on page 97.
Granger Causality: x granger causes y if a model that uses current and past values of x and current and past values of y to predict future values of y has smaller forecast error than a model than only uses current and past values of y to predict y. In other words, Granger causality answers the following question: does the past of variable x help improve the prediction of future values of y?
Instantaneous Causality: x instantaneously Granger causes y if a model that uses current, past and future values of x and current and past values of y to predict y has smaller forecast error than a model than only uses current and past values of x and current and past values of y. In other words, Instantaneous granger causality answers the question: does knowing the future of x help me better predict the future of y? If I know that x is going to do, does it help me know what y is going to know?
I know this is an old question, but I thought I would answer it in case someone else is struggling as I was with this.
The book goes deeply into the math of these two metrics, so please take a look at it if you want a more formal answer.
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1$\begingroup$ Can you give an example of when IGC is a useful concept? $\endgroup$– dimitriyCommented Jul 31, 2020 at 5:49
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$\begingroup$ It is p. 97, not 67 of the book. In the first edition, it is p. 95-96. $\endgroup$ Commented Jan 10, 2021 at 14:23
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$\begingroup$ @DimitriyV.Masterov I was thinking about using the IGC results to guide the construction of a coefficient restriction matrix for the structural VAR model (rather than relying on the Cholesky decomposition). I think this approach is more objective. $\endgroup$– Long VoCommented Apr 8, 2021 at 3:35