Say that there are two time series of highly correlated stocks one of which is the driver and the second one follows the first one.
What mathematical measure or formula would you use to identify which one is the driver and the follower?
What techniques have you tried?
You have to be quite careful in how you interpret the results, as there are constraints on what the possible factors of influence can be (when testing for Granger Causality).
The anwser is clear cut, there isn't one. The high correlation between the 2 stocks is explained by a common underlying risk factor, for example both 2 gold mining companies. This common factor explains the high correlation. The correlation doesn't mean that one 1 stock drives the other, meaning actual causation.
The best you can do is think about risk factors that could explain the high correlation and then use principle component analysis to select those which fit best.