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In 1975 James Pickands III showed that the excesses over a high threshold areapproximatly Generalized Pareto distributed. Since then, a variety ofestimators for the parameters of this cdf have been studied, but alwaysassuming the underlying data to be independent. In this paper we consider thespecial case where the underlying data arises from a linear process withregularly varying (i.e. heavy-tailed) innovations. Using this setup, we thenshow that the likelihood moment estimators introduced by Zhang (2007) areconsistent estimators for the parameters of the Generalized Paretodistribution.

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