• Bernoulli
  • Volume 15, Number 2 (2009), 325-356.

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

Moosup Kim and Sangyeol Lee

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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.

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Bernoulli, Volume 15, Number 2 (2009), 325-356.

First available in Project Euclid: 4 May 2009

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autoregressive process change point test cusum test extreme value theory Hill’s estimator mixing condition tail index tail sequential process


Kim, Moosup; Lee, Sangyeol. Test for tail index change in stationary time series with Pareto-type marginal distribution. Bernoulli 15 (2009), no. 2, 325--356. doi:10.3150/08-BEJ157.

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