In general, the finite sample behavior of the testing procedures does not seem to be strongly influenced by the tail parameter. An increase of dependence, i.e. increasing values of H , are usually followed by a decrease of the rejection rates though. 

We make the following observations with respect to the behavior of the different testing procedures: 

• The CUSUM test suffers from severe size distortions. It rejects the hypothesis too frequently for every combination of the considered parameters α and H . In par- ticular, the number of rejections increases as the number of observations increases. Apparently, unrealistically large sample sizes are required for the asymptotics to ap- ply. The same observation has been made in De Pooter and Van Dijk (2004), where the CUSUM statistic is used to test for breaks in the variance of GARCH(1, 1) time series. 

• The self-normalized CUSUM test tends to be undersized. 

• The Wilcoxon test rejects the hypothesis too often. Yet, the rejection rates seem to converge to the level of significance. 

• The empirical size of the self-normalized Wilcoxon test is close to the level of signif- icance. 

• The power of both Wilcoxon-based testing procedures does not depend on α . Con- trary to the behavior of the CUSUM test, the increase and decrease of the variance are almost equally well detected by both Wilcoxon tests. 

• The power of the Wilcoxon test exceeds the power of the self-normalized Wilcoxon test for every parameter combination that has been considered. 

All in all, the simulation results show that both CUSUM tests are outperformed by the Wilcoxon-based testing procedures: Although the CUSUM test has high size distortions, 

