No severe autocorrelation is found in the AEX-index. It is noteworthy that for most data series the second order autocorrelation is negative, while only in 8 out of 51 cases it is positive. The first order autocorrelation is negative in 10 cases. The Ljung-Box (1978) Q-statistics in the second to last column of table 4.3 reject for almost all data series the null hypothesis that the first 20 autocorrelations of the returns as a whole are equal to zero. For only 10 data series the null is not rejected. When looking at the first to last column with Diebold's (1986) heteroskedasticity-consistent Box-Pierce (1970) Q-statistics it appears that heteroskedasticity indeed seriously affects the inferences about serial correlation in the returns. When a correction is made for heteroskedasticity, then for the AEX-index and 41 stocks the null of no autocorrelation is not rejected. The autocorrelation functions of the squared returns show that for all data series the autocorrelations are high and significant up to order 20. The Ljung-Box (1978) Q-statistics reject the null of no autocorrelation in the squared returns firmly, except for steel manufacturer Corus. Hence, almost all data series exhibit significant volatility clustering, that is large (small) shocks are likely to be followed by large (small) shocks.
4.3 Empirical results
4.3.1 Results for the mean return criterion
Technical trading rule performance
In section 4.2 we have shown that almost no significant autocorrelation in the daily returns can be found after correction for heteroskedasticity. This implies that there is no linear dependence present in the data. One may thus question whether technical trading strategies can persistently beat the buy-and-hold benchmark. However, as noted by Alexander (1961), the dependence in price changes can be of such a complicated nonlinear form that standard linear statistical tools, such as serial correlations, may provide misleading measures of the degree of dependence in the data. Therefore he proposed to use nonlinear technical trading rules to test for dependence. In total we apply 787 objective computerized trend-following technical trading techniques with and without transaction costs to the AEX-index and to 50 stocks listed in the AEX-index (see sections 2.3 and 3.3 and
Appendix B of Chapter 3 for the technical trading rule parameterizations). Tables 4.4 and 4.5 show for each data series some statistics of the best strategy selected by the mean return criterion, if 0% and 0.25% costs per trade are implemented. Column 2 shows the parameters of the best strategy. In the case of a moving-average (MA) strategy these parameters are ``[short run MA, long run MA]'' plus the refinement parameters ``[%-band
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