I am learning about quantitative finance, and I am struck by how different it is from the techniques that make it into magazines and TV, particularly technical analysis. Specifically, if they say an indicator (RSI, TRIX, etc.) can predict even short term future prices, then you should be able to run some analysis to see if this was at least true in the past.
So my questions are:
If I wanted to learn the statistics used to calculate if there is any correlation between an indicator and any future price tendencies, what methods do I use?
Are any of these indicators known to have been verified quantitatively?