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

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 Aust. N.Z. J. Stat. 49, 69–77 (2007) are consistent estimators for the parameters of the Generalized Pareto distribution.