Test for tail index change in stationary time series with Pareto-type marginal distribution

The tail index, indicating the degree of fatness of the tail distribution, is an important component of extreme value theory since it dominates the asymptotic distribution of extreme values such as the sample maximum. In this paper, we consider the problem of testing for a change in the tail index of time series data. As a test, we employ the cusum test and investigate its null limiting distribution. Further, we derive the null limiting distribution of the cusum test based on the residuals from autoregressive models. Simulation results are provided for illustration.