Asymptotic normality of the likelihood moment estimators for a stationary linear process with heavy-tailed innovations

The authors recently proved in Martig and Hüsler (2016) that the likelihood moment estimators are consistent estimators for the parameters of the Generalized Pareto distribution for the case where the underlying data arises from a (stationary) linear process with heavy-tailed innovations. In this paper we derive the bivariate asymptotic normality under some additional assumptions and give an explicit example on how to check these conditions by using asymptotic expansions. Some finite sample comparisons are presented to investigate the bias and variance behavior for some of the estimators.