I'm looking for some direction on testing whether a simple entry signal has statistical significance.
Let's say this is my simple entry signal:
Buy when some indicator has a positive slope and is above zero on 3 time frames (5M,15M,60M)
Sell when the indicator has a negative slope and is below zero on 3 time frames.
How do I go about statistically testing this signal to see if there's any alpha to be extracted?
I was thinking something along these lines:
- plot the P&L distribution for the signal should it exit 1,2,3, N bars after the entry.
- plot the P&L distribution if the entry point had been random and the exit had been again 1,2,3, N bars after the entry.
I'm not really sure where to go from there.
How do I go about creating a "random" entry signal? Perhaps taking the time difference between the first and last quote and creating a pseudo random time to enter. The number of entries would have to be equal to the number of non-random signals created from the indicator. Also, I say pseudo random because it probably wouldn't be desirable if all these "random" signals happened to cluster in one short time interval.
Then, what characteristics of these distributions should I be looking for to establish if the indicator signal has any statistical significance in terms of potential alpha that can be extracted.
Any direction or reference would be appreciated. Being that there are so many different types of statistical tests that can be done, it's hard to find anything particularly relevant.