Abstract In this paper, we study the change point test for the tail index of scale-shifted processes. To this task, we propose two tests. The first is designed via examining the discrepancy between the two Hill estimators obtained from the observations before and after a preliminary change point...

Asymptotic properties of the harmonic moment tail index Estimator are derived for distributions with regularly varying tails. The estimator shows good robustness properties and stands out for its simplicity. A tuning parameter allows for regulating the trade-off between robustness and...

Pareto-type distributions are extreme value distributions for which the extreme value index γ0. Classical estimators for γ0, like the Hill estimator, tend to overestimate this parameter in the presence of outliers. The empirical influence function plot, which displays the influence that each...

This paper explores tests of the hypothesis that the tail thickness of a distribution is constant over time. Using Hill's conditional maximum likelihood estimator for the tail index of a distribution, tests of tail shape constancy are constructed that allow for an unknown breakpoint. The...

This note reconsiders divergent results on the extremal behaviour of German stock returns that have been published recently. In particular, investigations of this issue have arrived at different conclusions regarding the finiteness of the second moment of the return distributions. Here we apply...