On consistency of the likelihood moment estimators for a linear process with regularly varying innovations
Statistics Theory
2016-05-26 v2 Applications
Statistics Theory
Abstract
In 1975 James Pickands III showed that the excesses over a high threshold are approximatly Generalized Pareto distributed. Since then, a variety of estimators for the parameters of this cdf have been studied, but always assuming the underlying data to be independent. In this paper we consider the special case where the underlying data arises from a linear process with regularly varying (i.e. heavy-tailed) innovations. Using this setup, we then show that the likelihood moment estimators introduced by Zhang (2007) are consistent estimators for the parameters of the Generalized Pareto distribution.
Keywords
Cite
@article{arxiv.1507.03429,
title = {On consistency of the likelihood moment estimators for a linear process with regularly varying innovations},
author = {Lukas Martig and Jürg Hüsler},
journal= {arXiv preprint arXiv:1507.03429},
year = {2016}
}
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17 pages