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ter than expected, based on our earlier explorations of simple neural network models. In the current tests, the more encouraging results were almost certainly due to the large number of data points in the training set, which resulted from training the model across an entire portfolio, rather than on a single tradable. In general, the larger the optimization (or training) sample, the greater the likelihood of continued performance in the verification sample. Sample size could be increased by
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Out-of-Sample Results Broken Down by Test and Market
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going back further in history, which would be relatively easy to accomplish since many commodities contracts go back well beyond the start of our in-sample period (1985). It could also be increased by enlarging the portfolio with additional markets, perhaps a better way to bolster the training sample. A maxim of optimization is that the likelihood of performance holding up increases with reduction in the number of model parameters. Given the somewhat positive results obtained in some of the tests, it might be worthwhile to experiment
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Performance of Neural Network Models Broken Down by Model, Order, and Sample
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with more sophisticated models. Specifically, better input preprocessing, in the sense of something that could reduce the total number of inputs without much loss of essential predictive information, would probably lead to a very good trading system. With a smaller number of inputs, there would be fewer parameters (connection weights) in the network to estimate. Consequently, curve-fitting, an apparently significant issue judging by the results and shrinkage levels, would be less of a problem.
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WHAT HAVE WE LEARNED
Under certain conditions, even neural newbie models can work. The critical issue with neural networks is the problem of achieving an adequate ratio of sample size to free parameters for the purpose of minimizing harmful (as opposed to beneficial) curve-fitting. n Curve-fitting is a problem with neural networks. Any methods by which the total number of parameters to be estimated can be reduced, without too much loss of predictive information, are worth exploring; e.g., more sophisticated information-compressing input preprocessing would probably improve out-of-sample performance and reduce the effects of pemicious curve-fitting.
a For similar reasons, large samples are critical to the training of successful neural network trading models. This is why training on whole portfolios provides better results than training on individual tradables, despite the loss of market specificity. One suggestion is to increase the number of markets in the portfolio and, thereby, achieve a larger in-sample training set. Carrying this to an extreme, perhaps a neural network should be trained on hundreds of commodities, stocks, and various other trading instruments, in an effort to develop a universal market forecaster. If there are any universal technical price patterns that exist in all markets and that have predictive validity, such an effort might actually be worthwhile. . Some markets trade poorly, even in-sample. Other markets tend to hold up out-of-sample. This has been found with other models in earlier chapters: Some markets are more amenable to trading using certain techniques than are other markets. Selecting a subset of markets to trade, based on continued out-of-sample performance, might be an approach to take when developing and trading neural network systems.
C H A P T E R
T W E L V E
Genetic Algorithms
xtrapolating from models of biology and economics, mathematician/psychologist, John Holland, developed a genetic optimization algorithm and introduced it to the world in his book, Adaptation in Natural and Artificial Systems (1975). Genetic algorithms (or GAS) only became popular in computer science about 1.5 years later (Yuret and de la Maza, 1994). The trading community first took notice around 1993, when a few articles (Burke, 1993; Katz and McCormick, 1994; Oliver, 1994) and software products appeared. Since then, a few vendors have added a genetic training option to their neural network development shells and a few have industrial strength genetic optimization toolkits. In the trading community, GAS never really had the kind of heyday experienced by neural networks. The popularity of this technology probably never grew due to its nature. Genetic algorithms are a bit difficult for the average person to understand and more than a bit difficult to use properly. Regardless of their image, from our experience, GAS can be extremely beneficial for system developers. As with neural networks, while a brief discussion is included to provide basic understanding, it is not within the scope of this book to present a full tutorial on genetic algorithms. Readers interested in studying this subject further should read Davis (1991), as well as our contributions to the book Virflral Trading (Katz and McCormick, 1995a, 1995b) and our articles (Katz and McCormick, July/August 1994, December 1996, January 1997, February 1997).
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