# Granger causality and Wald test in multivariate non-stationary case

I have a list of market indices (like 20 indices) and want to analyse which indices are the most important for prediction of CDS of a company.

Most of the time series are I(1) processes. I was using Christoph Pfeiffer R code to test Granger causality for each market index and CDS.

I found that some indices Granger-cause CDS and some indices are cointegrated with CDS.

My next step is to perform Wald test on a more complicated VAR model with several market indices. I still need to understand how to do this (the series are not stationary). Here the list of questions I have:

1. Can I exclude market indices from the multivariate model, if in the bivariate models these indices do not Granger-cause CDS?

2. Can I compare market indices based on bivariate Granger test results?

3. How to select lags in the multivariate model for each variable?

• Could you illustrate what "a more complicated VAR model" is -- and what you intend to use it for (do a Wald test in order to..., what else)? It could be relevant with respect to answering your questions. – Richard Hardy Mar 22 '16 at 9:14
• I was going go set up a VAR model (VAR function in R) with multiple regressors (p lags for each index). Then I would apply Wald test for coeficients for each index (analogous to Toda-Yamamoto algorithm). But that sounds quite complicated. I have around 20 indexes (7 of them Granger cause CDF according to the bivariate test). The maximul lag in the bivariate models is 12. – Katja Mar 22 '16 at 9:39
• I see. Unless you have a large data set, the model complexity (the number of parameters to be estimated) will be an issue if you try to have all 20 indices with several lags each... – Richard Hardy Mar 22 '16 at 9:58
• Is it possible, that an index Granger-causes CDS in a multivariable model, but does not Granger-cause CDS in a bivariate model? – Katja Mar 22 '16 at 10:11
• Yes, that should be possible, unless the indices and their lags are uncorrelated (which is unlikely). – Richard Hardy Mar 22 '16 at 10:26