2.6 Bootstrap
2.6.1 Bootstrap tests: methodology
The results reported in the last section show again that simple trend-following technical trading techniques have forecasting power when applied to the LIFFE series in the period 1983:1-1987:12. In this section we investigate whether the good results found can be explained by some popular time series models like a random walk, autoregressive or an exponential GARCH model using a bootstrap method.The bootstrap methodology compares the percentage of trading rules with a significantly positive mean buy return, with a significantly negative mean sell return, with a significantly positive mean buy-sell difference and with a significantly positive mean buy as well as a significantly negative mean sell return, when applied to the original data series, with the percentages found when the same trading rules are applied to simulated comparison series. The distributions of these percentages under various null hypotheses for return movements will be estimated using the bootstrap methodology inspired by Efron (1982), Freedman (1984), Freedman and Peters (1984a, 1984b), and Efron and Tibshirani (1986). According to the estimation based bootstrap methodology of Freedman and Peters (1984a, 1984b) a null model is fit to the original data series. The estimated residuals are standardized and resampled with replacement to form a new residual series. This scrambled residual series is used together with the estimated model parameters to generate a new data series with the same properties as the null model.
For each null model we generate 500 bootstrapped data series. The set of 5350 technical trading rules is applied to each of the 500 bootstrapped data series to get an approximation of the distributions of the percentage of strategies with a significantly positive mean buy return, with a significantly negative mean sell return, with a significantly positive buy-sell difference and with a significantly positive mean buy as well as a significantly negative mean sell return under the null model. The null hypothesis that our strong results found can be explained by a certain time series model is rejected at the α percent significance level if the percentage found in the original data series is greater than the α percent cutoff level of the simulated percentages under the null model.