# VAR model and Granger causality issues

Is it necessary to create a stable vector autoregressive (VAR) model satisfying all the necessary checks to create it and then and only can we say that Granger causality holds true?

Yes. In the specific case of VAR models, imagine we want to test the restriction that $x$ does not Granger-cause $y$. We have the regression (in $y$): $$y_t=\alpha + \sum_{l=1}^p \delta_ly_{t-l}+\sum_{l=1}^q \gamma_lx_{t-l}+\epsilon_t$$ The corresponding null to our Granger causality test is $H_0:\gamma_l=0,\,\,l=1,\dots,p$. This is a Wald test, and under the asymptotic normality and consistency of your estimator, it is $\chi^2$ distributed. If your process is not covariance-stationary, the variance of $\epsilon_t$ might change over time so you're estimate will no longer be asymptotically i.i.d. normal and the test statistic may no longer be $\chi^2$ distributed.