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When considered over all models, the stop performed best in both samples. The worst performers were, in-sample, the open and, out-of-sample, the limit. In-sample, when considered over all order types, crossover with confirmation was the best. Outof-sample, the basic lunar crossover model performed best and crossover with contirmation worst. There were many strong interactions between sample, model, and order. Some of the results stem from the small number of trades. The best of the seasonal model-
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order combinations yielded better and more consistent performance than the best of the lunar ones.
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When entire portfolios are considered, entry models based on lunar rhythms do not do as well as those based on seasonal rhythms. The poor showing of the lunar effect contradicts our earlier study (Katz and McCormick, June 1997). The differences may stem from two possible factors: entry models and exits. In the current tests, the models were optimized on an entire portfolio, which may not be appropriate for the lunar rhythm (the earlier model entered the market a specified number of days after full or new moon). The methods used in this chapter were altered from the previous study because of the need to optimize using common parameters across all markets. Doing this with the earlier approach would require that trades be entered n-days after the full or new moon, regardless of the market being traded; since lunar rhythms are distinct for each market (as demonstrated in our previous study), this approach was inappropriate. The earlier model was, therefore, redesigned to be self-adaptive, i.e., as it proceeds through lunar cycles, the appropriate timing for trading is decided by analysis of previous lunar cycles. Another possible reason for the conflicting results may be the interaction between the exits and entries, The lunar model, and perhaps the seasonal model, has the property of pinpointing tradeable tops and bottoms, but only a percentage of the time. Such systems work best with very tight stops that quickly cut losses when predictions go wrong, but that allow profits to accumulate when correct. In general, the lunar models performed poorly, but there were individual markets with consistent, positive performance-encouraging, given the model was not optimized to them. Results suggest that some great systems are hiding here if entries were tailored to them, e.g., in our earlier study, the lunar model traded Silver well; in the current study, Silver was not strongly responsive. Although the lunar models lost money on the portfolio, they lost very much less on a per-trade basis than did, for instance, most moving average and oscillator entry models.
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SOLAR ACTIVITY AND TRADING
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An earlier study (Katz and McCormick, September 1997) examined the effects of sunspots on the S&P 500 and Wheat. In-sample, a simple sunspot model pulled $64,000 from the S&P 500 between 1984 and 1992. There were 67 trades, 31% profitable. The average winning trade was $5,304.76, much larger than the average loser (-$1,030.43). The average trade was $955.22 with a return of 561% (not annualized). The long side was profitable, but the short side was substantially more so, highlighting the tendency of unusual solar activity to coincide with market crashes. The better performance of short trades is especially significant, since this market
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was in a secular uptrend during most of the testing period. Profitability continued out-of-sample, from 1993 through 1996, with a 265% return, 23 trades (30% profitable), and with an average trade yielding $891.30. The results for Wheat were also good across samples. In-sample, 57% of X4 trades were profitable with a $203.27 average trade and 859% return (not annualized). Out-of-sample, there were 29 trades, 55% profitable, a $260.78 average trade, and 406% return. Our initial research suggested further study would be worthwhile. The tests below examine the effects of solar activity on the standard portfolio. Daily sunspot numbers from 1985 through 1999, from the Royal Observatory of Belgium, were used to generate entries.
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