R - Testing for Granger causality when OLS assumption are violated I am using the vars package to estimate a VAR-model. Since it seems, that the residuals of my model are neither homoscedastic or uncorrelated I computed Newey West Standard Errors to perform the t-tests for the individual coefficients of every model. Obviously the test results are different using the robust standard errors. Now I want to test for granger causality in the model.
I will try to structure my questions, 
How is the F-Test of causality() improved by using a robust covariance estimator?
According to the documentation of the vars package the causality() function divides the endogenous variables of the model in two groups and then tests whether one variable granger causes all the other variables in the model (as has been explained here). It does so by utilizing an F-Test.
The function offers to add a specification of the covariance matrix of the estimated coefficients using the parameter vcov to allow for specifically using a robust covariance-matrix estimator. However, in this thread it is mentioned, that the F-statistic is not influenced by Newey West Standard Errros.
How does the use of a robust covariance matrix improve the F-Test for granger causality then?
Can I use grangertest() even though it is not directly connected to my VAR-model?
Furthermore in the thread cited above, it is advised to use the Wald Test instead of the F-Test, when the OLS assumptions for the error terms are violated.
The function grangertest() of the lmtest package is simply a Wald Test according to the documentation. However, the function is not capable of checking for models with more than two dimensions. However, it also allows to set a robust covariance matrix estimatior as a parameter.
Since I am also interested in the pairwise relation between the variables, would it still be correct to simply use the corresponding variables in pairs of two to test for granger causality between them?
I am a little hesitant to simply use grangertest(), because as far as I can see it would not be related to my VAR-model.
If grangertest() cannot be used to test for pairwise causality between the variables, can the causality() function be adapted to do the same?
 A: A couple of datapoints to assist:

*

*The Wald-test applies an F-test methodology (it is a particular form of F-test where you restrict a series of coefficients to your selected value(s)). If it helps to avoid any confusion, just think of the granger causation as an F-test where the coefficients on all the lagged explanatory variables are set to zero (which is also a sub-set of a Wald test).


*The F-test is improved by using newey-west standard errors because without those adjustments, the F-test is being run on a flawed model that is not B.L.U.E.


*Unfortunately, many (most) statistical packages run a granger causation test on a very basic, unadjusted OLS model (so no adjustments for heteroscedasticity, no check for structural breaks, no checking for serial correlation, outliers, ARCH effects, etc). Think of it this way, you can run any test on your data, but if you suspected non-normal residuals, etc you wouldn't be confident in the conclusions. The granger analysis in most software just ignores all those usual complications. Which is why it is often preferable to build your own granger model (it is very simple, just do an OLS with lagged dependent variables, lagged explanatory variables and a constant), and then check your data for all the typical concerns: normality, stationary, heteroscedasticity, etc etc. Applying newey-west estimators in your OLS model is a good place to start.


*The F-test will often be affected by the SE adjustments. Without going into the matrix algebra, you run a simple OLS yourself with and without newey-west SEs and you can see the differences in the F-values when you impose the granger restrictions. This will be especially true in certain fields of study, such as, stock price returns.


*Granger tests and VARs are closely related and if your software does not perform the granger F-test / Wald restriction on your VAR you can easily design a granger causation test as an OLS that is equivalent to your VAR (a VAR is basically an OLS with lagged dependent and lagged explanatory variables, so you can perform the F-test restrictions in an equivalent OLS built from scratch if your software doesn't allow it on a VAR; the results will be identical to several dp).
Long story short: lots of problems with Granger causation. You can improve the results by checking for the standard statistical complications you would apply to any OLS model (which is often easier in an OLS built from scratch rather than starting with the software's granger test). And yeah, stay away from the built-in granger causation tests unless (1) you are confident that your model doesn't have any of the typical statistical issues, or (2) you are in a rush for time and just need something quick and easy (although, once you build a few granger causation models using OLS models, you will realize how quickly it can be performed and how the unadjusted results are so similar).
Bit of a tangent, and probably telling you what you already know but, just remember that no matter how good your granger model, it still doesn't prove causation. You will see lots of spurious granger causations in your lifetime. Always start and end your analysis with a theoretical framework for the model and take the results with a grain of salt. It is an interesting (and often useful) analytical framework but far from conclusive.
