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

TL;DR

This paper develops a statistical test based on the cusum approach to detect changes in the tail index of stationary time series with Pareto-type distributions, crucial for understanding extreme value behavior.

Contribution

It introduces a cusum test for tail index change in time series and derives its null distribution, including residual-based versions, supported by simulation results.

Findings

The cusum test effectively detects tail index changes.

Residual-based cusum test has accurate null distribution.

Simulation confirms the test's practical usefulness.

Abstract

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.