On consistency of the likelihood moment estimators for a linear process with regularly varying innovations

TL;DR

This paper proves that likelihood moment estimators are consistent for heavy-tailed linear processes, extending their applicability beyond independent data to dependent data with regularly varying innovations.

Contribution

It demonstrates the consistency of Zhang's likelihood moment estimators within the context of linear processes with heavy-tailed innovations, a setting previously unaddressed.

Findings

Likelihood moment estimators are consistent for heavy-tailed linear processes.

Extension of estimator validity from independent to dependent data.

Supports use of these estimators in more complex time series models.

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.