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What is the difference in terms of inference? Does Instantaneous captures the short term cause and effects?

Constantinos Rousos
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  • Some related threads can be found here, though perhaps they are of limited relevance. – Richard Hardy Apr 20 '19 at 17:08
  • 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? – Constantinos Rousos Apr 20 '19 at 17:14
  • 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. – Richard Hardy Apr 20 '19 at 17:18
  • @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? – Constantinos Rousos Apr 20 '19 at 17:31
  • 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? – Richard Hardy Apr 20 '19 at 18:12
  • @RichardHardy thanks I see from a previous comment that I am in a situation that I have to use error corrections terms in all of my equations(both for the stationary and non-stationary) variables. How do I even built such a model in R: do i need to enter an lm~ function with the coefficients of the error correction terms obtained from the Johansen test and the coefficients from a VAR model with the differentiated(I1) variables? Thanks – Constantinos Rousos Apr 21 '19 at 10:29
  • You can build it "manually" using the lm function. – Richard Hardy Apr 21 '19 at 18:49
  • @RichardHardy, sorry for asking yet another question. If my information criteria indicate p lags for the complete VAR model, but cointegration occurs at a lag <p should i include the rest of lags until p for the cointegrated variable or should I stop at the cointegrated lag. And if I stop there should i include all lags until p for my I0 variables? – Constantinos Rousos Apr 21 '19 at 21:15
  • I do not quite understand the situation you are describing. Cointegration does not occur at a particular lag; series are either cointegrated or not, and this does not change after we lag some series with respect to other series. – Richard Hardy Apr 22 '19 at 07:44
  • @ Richard Hardy I have 4 variables: 1)Volatility of Oil Prices 2) Volatility of Dow Jones Prices 3) Oil prices google trends series 4)Dow Jones google trends series

    Variables 1&3 are cointegrated at I1. Variables 2&4 are I0. When I take the first differences of 1&3 and use information criteria I find that VAR should be constructed at 2 lags.

     – Constantinos Rousos Apr 22 '19 at 12:26
  • VolOil.d= VolOil.dt-1+VolDJIAt-1+OilPricesgt.dt-1+DJIAgt-1+VolDJIAt-2+DJIAgt-2+ECT

    Is this correct for example?

     – Constantinos Rousos Apr 22 '19 at 12:50
  • The optimal lag order for all four variables might be different from the one for just two of them. Optimal lag order selection is nontrivial, so it is difficult to give a precise recipe of what you should do. Try some different orders and compare information criteria if you are able to calculate them (it will be messy since you do not have a standard model for which there would be a function extracting them for you). – Richard Hardy Apr 22 '19 at 12:50

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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.

Richard Hardy
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amilkar0417
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    Can you give an example of when IGC is a useful concept? – dimitriy Jul 31 '20 at 05:49
  • It is p. 97, not 67 of the book. In the first edition, it is p. 95-96. – Richard Hardy Jan 10 '21 at 14:23
  • @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. – Long Vo Apr 08 '21 at 03:35