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At the very least, you should have available an optimizer that is designed to make both brute force and user-guided optimization easy to carry out. Such an optimizer is already at hand if you use either TradeStation or Excalibur for system development tasks. On the other hand, if you develop your systems in Excel, Visual Basic, C+ +, or Delphi, you will have to create your own brute force optimizer. As demonstrated earlier, a brute force optimizer is simple to implement. For many problems, brute force or user-guided optimization is the best approach. If your system development efforts require something beyond brute force, a genetic optimizer is a great second choice. Armed with both brute force and genetic optimizers, you will be able to solve virtually any problem imaginable. In our own efforts, we hardly ever reach for any other kind of optimization tool! TradeStation users will probably want TS-Evolve from Ruggiero Associates. The
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Evolver product from Palisade Corporation is a good choice for Excel and Visual Basic users. If you develop systems in C+ + or Delphi, select the C+ + Genetic Optimizer from Scientific Consultant Services, Inc. A genetic optimizer is the Swiss Army knife of the optimizer world: Even problems more efficiently solved using such other techniques as analytic optimization will yield, albeit more slowly, to a good genetic optimizer. Finally, if you want to explore analytic optimization or simulated annealing, we suggest Numerical Recipes in C (Press et al., 1992) and Masters (1995) as good sources of both information and code. Excel users can try out the built-in Solver tool.
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M any trading system developers have little familiarity with inferential statistics. This is a rather perplexing state of affairs since statistics are essential to assessing the behavior of trading systems. How, for example, can one judge whether an apparent edge in the trades produced by a system is real or an artifact of sampling or chance Think of it-the next sample may not merely be another test, but an actual trading exercise. If the system s edge was due to chance, trading capital could quickly be depleted. Consider optimization: Has the system been tweaked into great profitability, or has the developer only succeeded in the nasty art of curve-fitting We have encountered many system developers who refuse to use any optimization strategy whatsoever because of their irrational fear of curve-fitting, not knowing that the right statistics can help detect such phenomena. In short, inferential statistics can help a trader evaluate the likelihood that a system is capturing a real inefficiency and will perform as profitably in the future as it has in the past. In this book, we have presented the results of statistical analyses whenever doing so seemed useful and appropriate. Among the kinds of inferential statistics that are most useful to traders are t-tests, correlational statistics, and such nonparametric statistics as the runs test. T-rests are useful for determining the probability that the mean or sum of any series of independent values (derived from a sampling process) is greater or less than some other such mean, is a fixed number, or falls within a certain band. For example, t-tests can reveal the probability that the total profits from a series of trades, each with its individual profitAoss figure, could be greater than some threshold as a result of chance or sampling. These tests are also useful for evaluating sanpies of returns, e.g., the daily or monthly returns of a portfolio over a period of years. Finally, t-tests can help to set the boundaries of likely future performance 51
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(assuming no structural change in the market), making possible such statements as the probability that the average profit will be between x and y in the future is greater than 95%: Correlational stnristics help determine the degree of relationship between different variables. When applied inferentially, they may also be used to assess whether any relationships found are statistically significant, and not merely due to chance. Such statistics aid in setting confidence intervals or boundaries on the true (population) correlation, given the observed correlation for a specific sample. ,Correlational statistics are essential when searching for predictive variables to include in a neural network or regression-based trading model. Correlational statistics, as well as such nonparamenic statistics as the runs test, are useful in assessing serial dependence or serial correlation. For instance, do profitable trades come in streaks or runs that are then followed by periods of unprofitable trading The runs test can help determine whether this is actually occurring. If there is serial dependence in a system, it is useful to know it because the system can then be revised to make use of the serial dependence. For example, if a system has clear ly defined streaks of winning and losing, a metasystem can be developed. The memsystem would take every trade after a winning trade until the tirst losing trade comes along, then stop trading until a winning trade is hit, at which point it would again begin taking trades. If there really are runs, this strategy, or something similar, could greatly improve a system s behavior. WHY USE STATISTICS TO EVALUATE TRADING SYSTEMS It is very important to determine whether any observed profits are real (not artfacts of testing), and what the likelihood is that the system producing them will continue to yield profits in the future when it is used in actual trading. While outof-sample testing can provide some indication of whether a system will hold up on new (future) data, statistical methods can provide additional information and estimates of probability. Statistics can help determine whether a system s performance is due to chance alone or if the trading model has some real validity. Statistical calculations can even be adjusted for a known degree of curve-fitting, thereby providing estimates of whether a chance pattern, present in the data sample being used to develop the system, has been curve-fitted or whether a pattern present in the population (and hence one that would probably be present in future samples drawn from the market being examined) has been modeled. It should be noted that statistics generally make certain theoretical assumptions about the data samples and populations to which they may be appropriately applied. These assumptions are often violated when dealing with trading models. Some violations have little practical effect and may be ignored, while others may be worked around. By using additional statistics, the more serious violations can sometimes be
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