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Trading Results for the Top Turning-Point Model
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The two networks that were selected as most likely to hold up out-of-sample, based on their corrected multiple correlations with the target, are analyzed for trading performance below. The first network was the smaller of the two, having 3 layers (18-10-l network). The second network had 4 layers (18-20-6-l network).
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Results of the 18-10-I Network. As usual, the in-sample performance was
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excellent. Out-of-sample performance was profitable for two of the orders: entry at open (Test 13) and on limit (Test 14). There were moderate losses for the stop order (Test 15). This is slightly surprising, given that the short side is usually less profitable than the long side. The market-by-market breakdown reveals that only the Canadian Dollar, Feeder Cattle, Bean Oil, Wheat, and Cocoa were not profitable across all three order types, in-sample. Out-of-sample, strong profits were observed across all three orders for the Deutschemark, the Japanese Yen, Light Crude, Heating Oil, Feeder Cattle, Live Cattle, and Corn. The Japanese Yen, Light Crude, and, to some extent, Corn shared profitability with the corresponding bottom (long) turningpoint model; in other words, these markets held up out-of-sample for both the bottom network and the top (short) network. The equity curve (Figure 1 l-2) for entry at open depicts rapidly rising equity until August 1993, and then more slowly rising equity throughout the remainder of the in-sample period and through about two-thirds of the out-of-sample period. Equity then declined slightly.
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Equity Growth for Short Turning Points, 18-l O-l Net, with Entry at Open
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Out-of-sample
equity
Results of the 18-20-6-I Network. As expected, this network, the larger of the two, produced greater and more consistent in-sample profits due to a higher amount of curve-fitting. Out-of-sample, this network performed terribly across all order types (at open, on limit, and on stop, or Tests 16, 17, and 18, respectively). The least bad results were obtained with the stop order. In-sample, only Silver, Wheat, Sugar, and Orange Juice did not trade profitably across all orders. Out-of-sample, only Cocoa showed profitability for all three orders. Surprisingly, all the metals showed strong out-of-sample profitability for the entry at open and on limit, as did Feeder Cattle, Cocoa, and Cotton. Portfolio equity showed incredibly smooth and steep gains in-sample, with losses out-of-sample for all order types. SUMMARY ANALYSES
Table 11-5 provides in-sample and Table 11-6 contains out-of-sample performance statistics for all of the neural network models broken down by test and market. The SYM column represents the market being studied. The rightmost column (COUiV~ contains the number of profitable tests for a given market. The numbers in the lirst row represent test identifiers. The last row (COUruT) contains the number of markets on which a given model was profitable. The data in this table provides relatively detailed information about which markets are and are not profitable when traded by each of the models: One dash (-) indicates a moderate loss per trade, i.e., $2,000 to $4,000; two dashes (--) represent a large loss per trade, i.e., $4,000 or more; one plus sign (+) means a moderate profit per trade, i.e., $1,000 to $2,000; two pluses (+ +) indicate a large gain per trade, i.e., $2,000 or more; and a blank cell means that the loss was between $0 and $1,999 or the profit was between $0 and $1,000 per trade. (For information about the various markets and their symbols, see Table II-1 in the Introduction to Part IL) In-sample, every order and every model yielded exceptionally strong positive returns (see Table 1 l-7). When averaged over all models, the entry at open and on limit performed best, while the entry on stop was the worst; however, the differences are all very small. In-sample, the best dollars-per-trade performance was observed with the large turning-point networks for the long (bottom) and short (top) sides. Out-of-sample, the stop order provided the best overall results. The time-reversed Slow %K and the short (top) turning-point models performed best when averaged across all order types. CONCLUSION When a neural newbie model was tested on an individual market (Katz and McCormick, November 1996), the conclusion was that such an approach does not work at all. The out-of-sample behavior in some of the current tests was much bet-
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