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Out-of-Sample Testing
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Another way to evaluate a system is to perform out-of-sample testing. Several time periods are reserved to test a model that has been developed or optimized on some other time period. Out-of-sample testing helps determine how the model behaves
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on data it had not seen during optimization or development. This approach is strongly recommended. In fact, in the examples discussed above, both in-sample and out-of-sample tests were analyzed. No corrections to the statistics for the process of optimization are necessary in out-of-sample testing. Out-of-sample and multiple-sample tests may also provide some information on whether the market has changed its behavior over various periods of time.
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Walk-Forward Testing
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In walk-forward testing, a system is optimized on several years of data and then traded the next year. The system is then reoptimized on several more years of data, moving the window forward to include the year just traded. The system is then traded for another year. This process is repeated again and again, walking forward through the data series. Although very computationally intensive, this is an excellent way to study and test a trading system. In a sense, even though optimization is occurring, all trades are taken on what is essentially out-of-sample test data. All the statistics discussed above, such as the t-tests, can be used on walkforward test results in a simple manner that does not require any corrections for optimization. In addition, the tests will very closely simulate the process that occurs during real trading--first optimization occurs, next the system is traded on data not used during the optimization, and then every so often the system is reoptimized to update it. Sophisticated developers can build the optimization process into the system, producing what might be called an adaptive trading model. Meyers (1997) wrote an article illustrating the process of walk-forward testing.
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CONCLUSION
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In the course of developing trading systems, statistics help the trader quickly reject models exhibiting behavior that could have been due to chance or to excessive curve-fitting on an inadequately sized sample. Probabilities can be estimated, and if it is found that there is only a very small probability that a model s performance could be due to chance alone, then the trader can feel more confident when actually trading the model. There are many ways for the trader to use and calculate statistics. The central theme is the attempt to make inferences about a population on the basis of samples drawn from that population. Keep in mind that when using statistics on the kinds of data faced by traders, certain assumptions will be violated. For practical purposes, some of the violations may not be too critical; thanks to the Central Limit Theorem, data that are not normally distributed can usually be analyzed adequately for most needs. Other violations that are more serious (e.g., ones involving serial dependence) do need to be taken into account, but rough-and-ready rules may be used to reckon corrections
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to the probabilities. The bottom line: It is better to operate with some information, even knowing that some assumptions may be violated, than to operate blindly. We have glossed over many of the details, definitions, and reasons behind the statistics discussed above. Again, the intention was merely to acquaint the reader with some of the more frequently used applications. We suggest that any committed trader obtain and study some good basic texts on statistical techniques.
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P A R T
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The Study of Entries
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Introduction
I n this section, various entry methods arc systematically evaluated. The focus is on which techniques provide good entries and which do not. A good entry is important because it can reduce exposure to risk and increase the likelihood that a trade will be profitable. Although it is sometimes possible to make a profit with a bad entry (given a sufficiently good exit), a good entry gets the trade started on the right foot.
WHAT CONSTITUTES A GOOD ENTRY A good entry is one that initiates a trade at a point of low potential risk and high potential reward. A point of low risk is usually a point from which there is little adverse excursion before the market begins to move in the trade s favor. Entries that yield small adverse excursions on successful trades are desirable because they permit fairly tight stops to be set, thereby minimizing risk. A good entry should also have a high probability of being followed quickly by favorable movement in the market. Trades that languish before finally taking off tie up money that might be better used elsewhere; not only do such trades increase market exposure, but they waste margin and lead to margin-ineffCent trading or portfolios. Perfect entries would involve buying the exact lows of bottoming points and selling the exact highs of topping points. Such entries hardly ever occur in the real world and are not necessary for successful trading. For trading success it is merely necessary that entries, when coupled with reasonable exits, produce trading systems that have good overall performance characteristics.
ORDERS USED IN ENTRIES Entries may be executed using any of several kinds of orders, including stop orders, limit orders, and market orders.
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