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This model is identical to the basic crossover model discussed earlier, except that entries were only taken if seasonal market behavior was contirmed by an appropriate reading of the Fast %K Stochastic. Specifically, if the seasonal crossover suggested a buy, the buy was only acted upon if the Fast %K was below 25%; i.e., the
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market has to be declining or near a bottom (as would be expected on the basis of the seasonal buy) before a buy can occur, Likewise, a seasonal sell was not taken unless the market was near a top, as shown by a Fast %K greater than 75%. As always, the standard exits were used. Entries were executed at the open (Test 7), on a limit (Test S), or on a stop (Test 9). Optimization for these tests involved stepping the length of the moving averages (avglen) from 5 to 20 in increments of 5 (PI) and the displacement (disp) from 0 to 20 in increments of 1 (P2). For entry at the open, a moving average length of 15 and a displacement of 7 were best. Entry on a limit was best with a length of 15 and a displacement of 6. Entry on a stop required a length of 20 and a displacement of 9. On a per-trade basis, the use of confirmation by the Fast %K worsened the results for both sampling periods when entry was at the open or on a limit; with both of these orders, trades lost heavily in both samples. When the confirmed seasonal was implemented using a stop order for entry, relatively profitable performance in both samples was seen. In-sample, the average trade pulled $846 from the market, while the average trade pulled $1,677 out of the market in the verification sample. In-sample, 41% of the trades were profitable and the annual return was 5.8%. The statistical significance is not great, but at least it is better than chance; both long and short positions were profitable. Out-of-sample, 44% of the trades were winners, the return on account was 19.6%, and there was a better than 77% chance that the model was detecting a real market inefficiency; both longs and shorts were profitable. Compared with other systems, the number of trades taken was somewhat low. There were only 292 trades in-sample and 121 out-ofsample. All in all, we again have a profitable model. Seasonality seems to have validity as a principle for entering trades. The equity curve for entry at open showed a gradual decline until May 1989. It was then fairly flat until August 1993, when equity began to decline through the remainder of the in-sample period and most of the out-of-sample period. The limit order was somewhat similar, but the declines in equity were less steep. For the stop order, the picture was vastly different. Equity declined at a rapid pace until May 1987. Then it began to rise at an accelerating rate, reaching a peak in June 1995, the early part of the out-of-sample period. Thereafter, equity was close to flat. The greatest gains in equity for the stop order occurred between June 1990 and May 1991, betweenMay 1993 and September 1993, and between January 1995 and June 1995. The last surge in equity was during the out-of-sample period. Compared with the previous two models, there were fewer markets with consistent profitability across all or most of the order types. Lumber was the only market that showed profitability across all three order types both in- and out-of-sample. Unleaded Gasoline yielded profits across all three order types insample, and was highly profitable out-of-sample with entry at open or on stop. Coffee and Cocoa were profitable for all order types in-sample, but profitable only for the stop order out-of-sample. For the stop order, the NYFE, Silver, Palladium,
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