I'm looking for the ideal independence test of two varaibles of unknown distribution, i.e. a non-parameteric test. Would choose between alternatives based on statistical power.
Few options that came to my mind are Kendall Tau and a test based on Spearman's rho. Chi-squared is an option, although power is a function of an additional parameter (binning), which makes it less compelling.
I wonder what other options are out there and how different options compare in terms of statistical power.
To give more color, I work in trading/finance, where forecasting relationships tend to be just as weak that it is difficult to find them. Once they are stronger, they quickly weaken to adhere to efficient market and no free lunch.
Relationships between variable do not have to be monotonic, but continuity of conditional mean or finite number of non-nontinuities is reasonable to assume.
We can assume iid-ness and typical sample size is 250 - 2500.