Finite sample behaviour of the mixed moment estimator in dependent frameworks

Abstract

In this paper, via Monte Carlotechniques and for dependent structures, likethe max-autoregressive processes and them-dependent processes, we explore the behaviorof a recently introduced extreme value indexestimator, the mixed moment estimator. Thedependent stationary sequences consideredprovide a wide spectrum of dependency, withan extremal index ranging from a value closeto one(as happens in identicallly distributedsettings, where exceedances of high thresholdsappear isolated)to any value smaller thanone, a situation in which exceedances ofhigh levels appear in clusters of a mean sizeapproximately equal to the reciprocal of thatextremal index.