# Statistical significance of trading systems that use indicators with long lookbacks

Let's say we have a trading system that trades daily, holding for one day, but uses an indicator that looks back over the last 5 years. A simple example could be the percent change in price of an asset over that 5-year period.

There will be a high degree of serial correlation in the indicator values from one day to the next, due to the overlap of the lookback. Are there standard ways of taking this into account when assessing the performance of a trading system?

Intuitively, it seems that for a fixed length of backtest data (say 10 years) we should have more certainty of our performance metrics, such as Sharpe, when we have short lookbacks, since then the samples of the indicator distribution are more independent. How do we quantify this? Or is it more of a rule-of-thumb situation?

-
Cross-posted on NP (already has one answer). – Joshua Ulrich Oct 16 '12 at 15:44
Your basic assumption is flawed. Quantity of historical data is independent of serial correlation. I work with trading firms whose model parameters are estimated from years of data, but the resulting signal has a half-life measured in hours. – pteetor Oct 16 '12 at 18:17
I don't think he's talking about quantity of backtesting data, but instead the timespan over which each value of the indicator is taken (the 'lookback'). If this lookback timespan is comparable in size to the backtesting timespan, then there will be strong serial correlation in the indicator. – mpeac Oct 16 '12 at 23:34
@pteetor - I'm not claiming any generalities here, and I agree that a high-turnover strategy could still make use of a parameter estimated over a long historical period. To illustrate my question, take for example the simple 'value' strategy from Asness et al, where they use a 5Y lookback, with over 30 years of data. Would their results be as significant on just 5 or 10 years of data? – andy Oct 17 '12 at 6:38

Running a look back of 5 years on a daily system equates to about 1260 look back points which seems awfully large. Obviously you will encounter serial correlation between indicator values when moving from one data point to the next. I highly recommend lowering the amount of data points that go into your indicator calculations.

A trading system has to first and foremost make intuitive sense before you perform any quantitative analysis. You also do not look back 50 days when looking to generate indicators for an intra day trading strategy. This has nothing to do with serial correlation yet or how you can quantify the optimal look back parameter. It has to do with your having to really understand what you actually try to measure and which dynamics you try to capture and how relevant the data points in the past are and how you want to weigh the different data points (because obviously the importance of the most recent data points is higher than older data points).

You seem to confuse the relationship of the amount of historical data over which you like to back test and its impact on your predictive power and rigor of analyzing a given strategy with the actual amount of data you utilize to calculate a single indicator data point. They are unrelated, completely unrelated from each other. I recommend you really attempt to segregate each concept and treat them entirely different.

1) The amount of data available to back test will need to be sufficient in order to give you the confidence that you tested the strategy over sufficiently different market cycles and market internals, in order to arrive at a better prediction of future performance as a function of past performance.

2) The amount of data point you utilize in the computation of an indicator point has a direct bearing on the performance and quality of your indicator signal and has nothing to do with the the relationship between a historical back test and its predictive power on future performance. This is an issue of optimization which in itself comes with a host of pitfalls that you need to pay attention to.

Only after a clear distinction between the two concepts do I recommend you to proceed.

This is my 2 cents from years of strategy development from anything mid-frequency to high frequency.

-