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I would like to take a closer look at stock prices and CDS spreads of different entities. Because both of them are nonstationary in levels, I use log stock returns and the first difference of the CDS.

My question: Can I run the Granger causality test on the Vector Autoregressive model (VAR) with the included variables in differences? And do I have to check for cointegration at first (and use a VECM)?

Help is very much appreciated.

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  • $\begingroup$ Check the extensive blog post by Dave Giles, "Testing for Granger Causality", then let us know if anything is still unclear. $\endgroup$
    – Richard Hardy
    May 30, 2017 at 16:56
  • $\begingroup$ I read that article (all his posts about GC to be exact, including "C to Shining C" and "VECM vs VAR") before I asked the question. I understand that we should normally model it in levels when using GC. However, my question is whether it makes sense to model stock prices (hence I asked it here on the quant fin board) instead of log stock returns (not diff), when we are interested in returns. I get that when I am interested in X, I should just leave it in levels even if nonstationary. I wanted to ask whether it still makes sense to model it like that when I am interested in the return itself. $\endgroup$
    – Kuma
    May 30, 2017 at 18:43
  • $\begingroup$ This is to contrast the subject-matter problem to the statistical problem. From the statistical perspective, to ensure the validity of your results, you need to follow sound statistical practice (e.g. as described in Dave Giles' blog). How to interpret the results comes in second. Fortunately, if you assume (and preferably validate the assumption by testing) that the logs of stock prices are cointegrated, you can use VECM where the dependent variables will be the log-returns. $\endgroup$
    – Richard Hardy
    May 30, 2017 at 20:03
  • $\begingroup$ Thanks for your answer! Modeling log stock returns as VAR/VECM and when testing for Granger causality, I use the procedure suggested by Prof. Giles (cointegration does not matter when testing GC); testing GC for stock prices (not in logs) and interpreting the results "as if" we would've used returns. Just to be sure about it: Is that more or less correct? $\endgroup$
    – Kuma
    May 31, 2017 at 6:39
  • $\begingroup$ Your statement is not precise enough (IMHO) to tell whether it is correct. Once again, even if you have a valid statistical result, you may still have a wrong interpretation. What exactly is the statement you are making there (when interpreting the results)? $\endgroup$
    – Richard Hardy
    May 31, 2017 at 7:01

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Regarding testing for Granger causality in presence or absence of cointegration, I find the extensive blog post by Dave Giles "Testing for Granger Causality" very helpful.

[M]y question is whether it makes sense to model stock prices <...> instead of log stock returns (not diff), when we are interested in returns. I get that when I am interested in X, I should just leave it in levels even if nonstationary. I wanted to ask whether it still makes sense to model it like that when I am interested in the return itself.

Let me contrast the subject-matter problem to the statistical problem. From the statistical perspective, to ensure the validity of your results, you need to follow sound statistical practice (e.g. as described in Dave Giles' blog). How to interpret the results comes in second. Fortunately, if you assume (and preferably validate the assumption by testing) that the logs of stock prices are cointegrated, you can use VECM where the dependent variables will be the log-returns.

Just to be sure about it: Is that more or less correct? <...> "Stock returns Granger cause spread changes"; this is the interpretation I had in mind (well, after checking whether there is Granger causality of course). The data to be used are stock prices and spreads.

I think your interpretation is fine.

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