In this research we presented a system for combining the different types of predictions given by a wide category of mechanical trading rules through statistical learning methods such as Boosting, and several model averaging methods such as Bayesian or Committee (simple averaging methods). The classical combining predictions procedure was useless because of the singularity of matrices involved. Besides, in order to avoid costly overactive technical trading rules derived from the boosting and the other learning methods, we introduced a fi lter which discards low-tuned buy-or-sell signals. The idea of using a fi lter to reduce trading frequency and to obtain higher returns is very old in Finance, and the success of the fi lters would justify the existence of some systematic trends in the prices which are not explained by the random walk model.
We have considered a sample consisting of 10 annual periods, from 1993 to 2002, in the NYSE Composite Index. Also, in order to give our work a deeper economic motivation which could suggest their transcendence and applications, we have repeated our experiment in two special rising and falling subsamples. The fi rst one was the rising subperiod until 1 September 2000. The second one was the falling subperiod after 1 September 2000.
Our fi rst conclusion is that, in general, improvements using a fi lter are not produced for all the statistical learning methods and periods analysed, with the exception of the fi ltered Boosting model, which always overcomes the non-fi ltered boosting. The fi ltered Boosting model also overcomes the rest of the fi ltered and non-fi ltered learning methods, in all the periods analysed, with the exception of the rising period from 1993 to 1 September 2000.
During short time periods some individual moving average rules could be more profi table than the fi ltered Boosting model, but this result inverts for longer time periods. Our results therefore suggest that the fi ltered Boosting model supplies better out-of-sample statistical and economic results than most of the single moving average rules during 10 annual periods, from 1993 to 2002 in the NYSE Composite Index. When we consider the complete 10-year period, the fi ltered Boosting model overcomes the best moving average with respect to several statistical and economic fi tness measures considered. Furthermore, the fi ltered Boosting model considerably improves the net returns of the B&H strategy and its Sharpe ratio.
By combining the predictive information of a wide set of rules we also reduce the data-snooping bias introduced by the arbitrary selection of parameters in the technical trading rules, avoiding the element of subjectivity that this procedure involves. Besides, the moving averages have a contingent predictive power, and its capacity for obtaining positive returns could be time varying. Thus the best moving average rule of the present year could be a bad one the following year, being impossible to establish, a priori, which are the best rules. Therefore, the Boosting and other learning methods are able to prevent the predictive mismatching which exists between different technical trading rules, providing new rules capable of using all the information offered for a broad category of rules.
During the complete period analysed (1993–2002), the fi ltered Boosting algorithm showed a high capability for obtaining the predictive information as much from good rules as from bad moving average rules, being more robust and profi table than any moving average rule for long time periods.
During the period of generalized rises (until 1 September 2000), neither the statistical learning method nor the moving average trading rule was able to obtain a net return higher than the return of the B&H strategy. In this subperiod the best ideal profi t ratio was also obtained by the B&H strategy, and the best Sharpe ratio was obtained by the moving average [10, 90, 2], followed by the B&H strategy.
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