I have an enquiry regarding the Granger Causality analysis. It is said that it is performed to check whether “X causes Y”, or to put it differently, whether X contains any predictive information with regards to Y and it mainly builds two regression models (one nested to other).

The first model (unrestricted) regresses Y against lagged values of Y and lagged values of X while the second model (restricted) regresses Y against lagged values of Y. It then uses a nested F test to compare the two models and draw conclusions.

Thus I am wondering, what’s the difference between this and a time series linear regression model which uses lagged values of the same variables for making predictions. In case a significant predictor is found, can one use the respective unrestricted model for prediction purposes?

Here is a "picture" of what I need to do (it may be easier for you to realize which point I fail to understand):

I have a DJIA closing values time series and I also have several different sentiment time series extracted from Twitter (for instance positive to negative tweets ratio). I need to assess whether integrating such sentiment time series in a predictive model, improves the prediction accuracy. Firstly I “stationarize” my time series and following I conduct a Granger causality analysis so as to determine whether these carry any predictive information about the DJIA closing values.

Following, I need to build a predictive model. Based on my understanding at the moment, an ARIMAX model would be appropriate for this task. So I thought I should deploy a predictive model which will include both past DJIA values and some of the sentiment time series as predictors. My question is how to build such a model and how is this going to be different from the unrestricted model I will have already used in the GCA.

Moreover I am not sure how to decide on which of the time series should I use as predictors and how to decide on the lags I need to include for both the AR and the MA part.

Thank you in advance for your help.

  • $\begingroup$ I don't quite understant your question: what’s the difference between this and a time series linear regression model which uses lagged values of the same variables for making predictions. $\endgroup$ – Richard Hardy Aug 4 '15 at 15:41
  • $\begingroup$ Please see in my answer. I wasn't able to post it as reply because it was too long. Thanks $\endgroup$ – Demetris Aug 5 '15 at 19:07
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    $\begingroup$ It might help for you to edit your original question, incorporating what you've presented in your answer into the question, then remove your answer. You can always edit your own question. If people browsing this site see that your question has an answer, they might skip it over thinking that you've already received the help you need. $\endgroup$ – EdM Aug 5 '15 at 19:16
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    $\begingroup$ Some comments on your answer. 1. MA in ARMA stands for lagged model errors (which are unobserved), not any exogenous variable. If you want to include an exogenous variable, use ARIMAX models or regression with ARMA errors. 2. It would make most sense to use the same model both for Granger causality testing and forecasting. (If you find Granger non-causality, then use the restricted version of the model.). Using one model for Granger causality testing and another model for forecasting is weird, especially when the purpose of Granger causality testing in your case is to help forecasting. $\endgroup$ – Richard Hardy Aug 6 '15 at 8:12
  • $\begingroup$ Thank you all for your comments and help. Yeah you are right about MA hadn’t realize that. Could you please elaborate a bit more on the ARIMAX models? I suppose this is what I tried to describe previously, namely, integrating both past data and exogenous variables, right? However I still fail to understand how is this going to be different from the GCA unrestricted model. On my understanding I will have to examine each of the exogenous variables separately in several bivariate(?) GCA tests. $\endgroup$ – Demetris Aug 6 '15 at 13:28

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