Granger causality is a standard statistical technique for determining whether one time series is useful in forecasting another. It is important to bear in mind that the term causality is used in a statistical sense, and not in a philosophical one of structural causation. More precisely a variable A is said to Granger cause B if knowing the time paths of B and A together improve the forecast of B based on its own time path, thus providing a measure of incremental predictability. In our case the time series of interest are market measures of returns, implied volatility, and realized volatility, or variable B. . . . Simply put, Granger's test asks the question: Can past values of trader positions be used to predict either market returns or volatility?

A report on Granger causality, discussed by Andrew Gelman at Statistical Modeling...

AG:

I have nothing to say on the particulars, as I have no particular expertise in this area. But in general, I'd prefer if researchers in this sort of problem were to try to estimate the effects of interest (for example, the amount of additional information present in some forecast) rather than setting up a series of hypothesis tests. The trouble with tests is that when they reject, it often tells us nothing more than that the sample size is large. And when they fail to reject, if often tells us nothing more than that the sample size is small. In neither case is the test anything like a direct response to the substantive question of interest.