I like Acrary's methods.
In modern statistics, Monte Carlo randomization types of tests are quite important and powerful. In my opinion, these types of things which can get at the real problem at hand, as opposed to a perfect analytic solution for a problem which isn't really the right one.
You can, at a simple level, attempt bootstraps of your actual returns (bootstraps are a randomized sequence taken from the original time series, and you should probably use a method which includes whatever sequential correlation appears to exist) and then compare to bootstraps of returns from a "null" (zero expectation) series.
You can get the second from randomized trading, or even just subtracting the sample mean of returns from yours (though that is 'less independent' in some ways).
Then a figure of merit could be the fraction of times, and degree that bootstrapped returns (or cumulative sum thereof, or some measure including drawdowns) exceed the simulated returns from a no-skill setup.
In modern statistics, Monte Carlo randomization types of tests are quite important and powerful. In my opinion, these types of things which can get at the real problem at hand, as opposed to a perfect analytic solution for a problem which isn't really the right one.
You can, at a simple level, attempt bootstraps of your actual returns (bootstraps are a randomized sequence taken from the original time series, and you should probably use a method which includes whatever sequential correlation appears to exist) and then compare to bootstraps of returns from a "null" (zero expectation) series.
You can get the second from randomized trading, or even just subtracting the sample mean of returns from yours (though that is 'less independent' in some ways).
Then a figure of merit could be the fraction of times, and degree that bootstrapped returns (or cumulative sum thereof, or some measure including drawdowns) exceed the simulated returns from a no-skill setup.

