I read the Euan Sinclair's book (Volatility trading) in which he suggests different volatility estimators (Close-to-close, Parkinson, Garman-Klass, ...).
I am inquiring about what is the best stock volatility measure to explain, let's say, the stock price returns.
Let's suppose that I want to test the effect of stock market volatility changes on stock market returns using the following model:
R(t) = α + β*VOL(t) + ε(t)
where R(t) is the stock returns in time t and VOL(t) is the volatility in time t. As suggested by Sinclair, there're different volatility measures. My question is what proxy measure I choose among all to describe in the best way this relationship among volatility and stock returns.
Does it makes sense to regress the stock returns on the single volatility measures and so to compare the related t-statistics (or p-values) and the R^2 of each model?
Or does there exist a statistical technique to do this?
Thanks for all the help you'll give me.