I have a couple of time series, say, T1 and T2. I have established (using the
grangercausalitytest library of
Statsmodels in Python) that T1 Granger-causes T2 at 10% significance for lags 4 and 5. I now want to know whether I can validate the result by using VAR (unrestricted model).
Going by the definition of Granger causality mentioned in the book "Introduction to Modern Time Series Analysis", for 2 time series, "x" and "y",
...if future values of y can be better predicted, i.e. with a smaller forecast error variance, if current and past values of x are used,
I should get less RMSE for the VAR model as compared to the Autoregression model with only T2. (I'm using ARIMA(p,0,0) for autoregression with p = 4,5 as the Granger - cause occurs at these lags)
My first question is my interpretation correct?
If not, why not? And if that is the case, the RMSE of what should I be comparing? I ask this question because T1 Granger-causes T2 at lags 4 and 5. Should I take the RMSE (for both VAR and Autoregression models) after lags of 4?
Also, should there be any other caveats?