comparison of the testing procedures, it is important to note that the finite sample results are based on simulations which were executed under the assumption that the normalization of the non-self-normalized tests and the multiplicative quantities that appear in the limits of the corresponding test statistics are known. In particular, normalization and limit of the non-self-normalized statistics usually depend on H , m , the slowly-varying function L$_{γ}$ that characterizes the autocovariances of the Gaussian random variables Y$_{j}$ , j ≥ 1, the distribution of ε$_{j}$ , j ≥ 1, (or at least the tail parameter α ), and the function σ . For all practical purposes these quantities are unknown, and for this reason have to be estimated. In contrast, the self-normalized test statistic can be computed from the given data while its limit depends on the parameters m and H only. For an adequate comparison of the testing procedures this has to be taken into consideration. Moreover, the simulation results show that the choice of the change-point test depends on the particular test situation that is considered. In general, an application of Wilcoxon- type tests reduces the influence of heavy tails in data generating processes on test decisions. In fact, we have seen that Wilcoxon-based testing procedures yield better results than CUSUM tests when testing for changes in mean and variance. This section contains supplementary material. In Section S1 the proof of Lemma 3.6 is presented; Section S2 comprises the full set of simulation results, i.e. in addition to the results presented in the main document, the simulation tables in Section S2 contain the empirical power of the testing procedures for changes located after a proportion τ = 0 . 25 of the data. Supplementary Material 34