What if series are not cointegrating what if there are four series all non stationary at level 0 but all stationary at level 1 but they are not co integrating can we still go granger causality and which granger causality var or vecm
 A: If all series are $I(1)$ but not cointegrated, you should estimate a VAR in first-differences. From there, you can test for granger causality. To test if $y_k$ granger causes $y_j$, you would test the hypothesis that all coefficients for $y_k$ in the $y_j$ equation are zero. 
A: Suppose you have a vector process $\, y_t$ of $I(1)$ variables that are not cointegrated (i.e. a "pure unit root" vector process).
Granger causality test for differences
Granger causality among variables in $\Delta y_t$ can be tested by 
fitting a VAR model to $\Delta y_t$ and including $y_{t-1}$ on the right hand side of the regression. In other words, regress the first difference $\Delta y_t$ on its lags as well as $y_{t-1}$.
The F-statistics for testing restrictions involving lags of $\Delta y_t$ (but not the lagged level $y_{t-1}$) has the usual $\chi^2$ asymptotic distribution.
In particular, Granger-causality among $\Delta y_t$ can be tested in the usual way.
Under the maintained hypothesis that there's no cointegrating relationship, the coefficient estimate on $y_{t-1}$ is super-consistent, and converges to zero. So strictly speaking, if you drop $y_{t-1}$ from the regression, the asymptotic distribution of F-statistics remain the same. But including $y_{t-1}$ improves finite sample performance.
This procedure is really a just a vector analogue of the Augmented Dickey-Fuller regression.
Granger causality test for levels
Alternatively, the question at hand is Granger-causality among levels, not differences.
Granger causality among variables in $y_t$ can be tested by 
fitting a VAR model to $y_t$, with one more lag.
In other words, if AIC/BIC/etc selects VAR($p$) for $y_t$, add one more lag and make it VAR($p+1$).
The F-statistics for testing restrictions involving first $p$ lags of $y_t$ (but not the $p+1$ lag $y_{t-p-1}$) has the usual $\chi^2$ asymptotic distributions.
In particular, Granger-causality among $y_t$ can be tested in the usual way.
This is the Toda-Yamamoto procedure. The last lag $y_{t-p-1}$ is inserted in the regression so that the F-statistics involving first $p$ lags of $y_t$ has standard 
asymptotic distributions. 
This is not restricted to $I(1)$ variables. For a vector process of $I(2)$ variables, add 2 additional lags, etc.
