Change point test for tail index of scale-shifted processes

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 estimate. The second is a modified recursive test which uses scale-adjusted observations. Both methods produce a tail index estimator that outperforms the Hill estimator. A simulation study and real data analysis are provided for illustration.