Should I back-test in a single (original) price series and bootstrap the strategy returns to get statistics of interest? Or should I create bootstrapped price series using bootstrapped returns from the original price series and run the strategy on those? The latter one requires significantly more computational power.
Straight bootstrap of the returns of the strategy would result in inconclusive evidence about the ability of the strategy to generate added value in terms of some "abnormal" returns. Bootstrapping original time series would undermine ability of the strategy to generate returns even if the strategy is reasonable. You could instead use solution in the style of Cowles, described above. For example, something like that:
- Model distribution of number of bars between two signals (buy and sell) of the actual strategy.
- Generate N buy/sell pairs from the distribution (1) and apply it to random points in time series.
- Finally, calculate equity curve and all statistics like profit factor, average drawdown, Ulcer and Sharpe ratio, etc.
- Repeat (2) and (3) many times, say B = 10 000+ times.
- Compare actual metrics and bootstrapped ones.