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

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

2009-06-11

arxiv.org/abs/0906.2037v1

Bernoulli 2009, Vol. 15, No. 2, 325-356

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ157 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ157

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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