  A variety of estimators for the parameters of the Generalized Pareto
distribution, the approximating distribution for excesses over a high
threshold, have been proposed, always assuming the underlying data to be
independent. We recently proved 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.
