Improving Moving Average Trading Rules with Boosting and Statistical Learning Methods, страница 7

^a  Parameters of the moving average rule [n₁, n₂, b]. ^b  Number of moving averages (minor : equal : major).

The classical combining predictions procedure was useless because of the singularity of matrices involved.

In Table I we show several statistical and economic characteristics of the forecasts corresponding to percentage of successful sign predictions, the net return, the ideal profi t ratio and the Sharpe ratio corresponding to the period of 10 years from 1993 to 2002.

All these statistical and economic characteristics are considered for the best and worst moving averages (below, in square brackets, the lengths of short and long moving averages and the band are presented), and for all fi ltered and non-fi ltered learning methods, that is, the Boosting model (fi ltered and non-fi ltered), the Committee moving average model (fi ltered and non-fi ltered) and the Bayesian moving average model (fi ltered and non-fi ltered). Below, in parenthesis, the number of moving average rules with minor, equal or major returns, respectively, is presented.^[2] In the last row of Table I, we have also shown the buy-and-hold strategy (B&H), in order to make comparisons.

The fi rst column in Table I shows, for every one of the forecasting procedures signalled above, the percentages of correct daily forecast direction. Column 2 shows the net return obtained by a technical strategy based on the signals obtained by the forecasting. We also show at the bottom, in parenthesis, the numbers of moving average rules with minor, equal or major returns, respectively.

Finally, in order to evaluate the performance of our technical trading rules we have also considered in columns 3 and 4 the ideal profi t ratio and the Sharpe ratio corresponding to all the forecasting procedures previously mentioned (at the bottom, in parenthesis, the number of moving average rules with minor, equal or major ideal profi t ratio and Sharpe ratio, respectively are presented).

Looking at Table I the following results stand out. The only model which overcomes the B&H strategy is the Boosting fi ltered model. Thus the net return, the ideal profi t ratio and the Sharpe ratio of the technical trading rule guided by the Boosting fi ltered model are 74.00%, 0.0508 and 0.0508, respectively, which overcomes any moving average rule and any other learning method. It even overcomes the net return, the ideal profi t ratio and the Sharpe ratio of B&H strategy, which are 67.33%, 0.0462 and 0.0279, respectively.

Besides, observe that the introduction of the fi lter improves the net return and the benefi t ratios in the Boosting and the Bayesian models. Nevertheless, the results in the Committee model worsen when a fi lter is employed.

Finally, observe that the maximum percentage of forecasting direction success is obtained by the best moving average rule [10, 140, 3], which is 52.02% successful. Therefore, although the success rates of forecasting the direction of the models reported in Table I are all slightly above 50%, some experience a higher Sharpe ratio than the B&H strategy, which means that these trading rules are, on average, correct when it matters more.

Following Table I the trading rule obtained by the fi ltered Boosting model overcomes the best moving average [5, 160, 6] with respect to any economical fi tness measure. Also observe that the Boosting, Bayesian and Committee models have been obtained ex ante. Meanwhile the best moving average was obtained ex post and so it is possible that its predictive power could even be inferior when we use it ex ante in a future period.

Now the ex ante capacity of moving averages to obtain benefi ts is studied. At this point our main concern is how the profi tability and predictive power of the moving average rules vary over time. This concern is directly related, as Sullivan et al. (1999) point out, to the dangers of data snooping, which are immense when we select the ‘best’ trading rule because, if suffi cient trading rules are considered over time, some rules are bound by pure luck, even in a very large sample, to produce a superior performance even if they do not genuinely possess predictive power over asset returns.