I'm looking to conduct hypothesis tests on some of my trading signals to see if the signal returns are statistically significant enough to falsify my null hypothesis that the signal has no predictive power.
A signal's returns can be distorted by 2 things: (1) the signal's long/short position bias, and (2) the market's net trend during the back-test period. Both of these components can apparently be eliminated by de-trending the data.
An excerpt from "Evidence Based Technical Analysis" : "To perform the detrending transformation, one first determines the average daily price change of the market being traded over the historical test period. This average value is then subtracted from each day's price change." He goes on to say to use log returns over percentage-based returns.
A few question arise:
1) What if my strategy is intraday, should I still be using the average DAILY price change to detrend the data, or should I go down to the frequency on which I trade and calculate the average 1 minute price changes (strategy trades on 1M)?
2) Should I really be using a future statistic (the average price change of the market over the backtest period) that is not known until the backtest is complete to detrend past data, post-backtest? I fear this will result in a statistical conclusion that is only valid for the backtest period. Or should I calculate the detrended market return every bar? In that case should I use a cumulative or rolling window to calculate the average market return (to be subtracted from the current return)?
3) I know there's other ways to detrend data other than:
( Log(CurrentPrice/LastPrice) - Average(Log(CurrentPrice/LastPrice)) )
Does anyone know of a method that is particularly better suited for my problem domain?