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ArticleOriginal scientific text

Title

On the tail index estimation of an autoregressive Pareto process

Authors 1

Affiliations

  1. Center of Mathematics of Minho University, Campus de Gualtar, 4710 - 057 Braga, Portugal

Abstract

In this paper we consider an autoregressive Pareto process which can be used as an alternative to heavy tailed MARMA. We focus on the tail behavior and prove that the tail empirical quantile function can be approximated by a Gaussian process. This result allows to derive a class of consistent and asymptotically normal estimators for the shape parameter. We will see through simulation that the usual estimation procedure based on an i.i.d. setting may fall short of the desired precision.

Keywords

ENG
extreme value theory, autoregressive processes, tail index estimation

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Discussiones Mathematicae Probability and Statistics
2013/33/1-2
Export to PBN, Opens in new tab
Pages:
65-77
Main language of publication
English
Received
2013-03-09
Accepted
2013-09-16
Published
2013

DOI: 10.7151/dmps1149

Exact and natural sciences