Using Statistics With Trading Systems: by Jeffrey Owen Katz, Ph.D., and Donna L. McCormick
In part 1, Katz and McCormick looked at the underpinnings
of how statistics can help the trader determine the feasibility of a system. This month, in part 2, they explain the steps necessary to evaluate trading system behavior with the use of statistics.
Last month, I laid the groundwork for how statistics can help the trader determine whether the per-formance of a system is due to chance, or if the trading model is valid. I explained how to use samples to make inferences about the populations from which they are drawn. Another issue I addressed was that of optimization — improving system performance by adjusting its parameters until the system performs its best on what the developer hopes is a representative sample. If the result is sufficiently good or the sample on which it was based sufficiently large so as to bring the probability of getting something by chance alone down to a sufficiently small value, there may still be a very significant result, even if many parameters have been optimized.
Next, I presented two examples. First, I optimized a system
on one sample of data (the in-sample data) and second, I ran
the system on another sample (the out-of-sample data), in
both cases calculating a variety of statistics. I used the lunar model trading system from my “Lunar cycles and trading”
STOCKS & COMMODITIES article, the TradeStation code for
which can be found in Figure 1. I used the Standard & Poor’s
500 index as the market, employing end-of-day, continuous
contract data. First, let’s recap the two examples introduced
in the last issue and the information pertinent to both, after which I will interpret the results.