Granger Causality test pre-conditions I am trying to analyse the causation between individual stock returns and index returns. I have taken the log return values of both stock and index values. Unit root test suggest that the values are stationary; but Johansen cointegration test resulted with two cointegrating equations in both Trace and Eigenvalues. 
Can I apply Granger causality test?
 A: If you have two time series, then the univariate unit-root test results coincide nicely with the cointegration test results. Both indicate that the series are stationary. Moreoever, this is as expected; financial returns are normally considered not to have unit roots.
However, you could think about cointegration between the stock price and the level of the stock index. They will both be integrated of order one (as they are cumulative sums of processes that do not contain unit roots, as per your current analysis), so there is at least the theoretical potential for cointegration. Whether cointegration would make sense in practice is another question and depends on the application. Here your subject-matter expertise will come in handy.
In any case, once you decide on presence/absence of cointegration between the stock price and the level of the stock index, you can proceed to Granger causality testing. 


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*In case of cointegration you would use the Toda-Yamamoto procedure described clearly in Dave Giles blog post "Testing for Granger Causality". 

*In case of no cointegration, you may run a simple vector autoregression and test for Granger causality in the regular way.

