Finite sample behaviour of the mixed moment estimator in dependent frameworks

Abstract

In this paper, via Monte Carlo techniques and for dependent structures, like the max-autoregressive processes and the mdependent processes, we explore the behavior of a recently introduced extreme value index estimator, the mixed moment estimator. The dependent stationary sequences considered provide a wide spectrum of dependency, with an extremal index ranging from a value close to one (as happens in identicallly distributed settings, where exceedances of high thresholds appear isolated) to any value smaller than one, a situation in which exceedances of high levels appear in clusters of a mean size approximately equal to the reciprocal of that extremal index.

The PORTSEA (Portuguese School of Extremes and Applications) and a few personal scientific achievements

“…n (k) respectively defined in (10) and in (12); [51], by Caeiro and Gomes, on probability weighted moments (PWM) estimation; [268], by Gomes and Stehlík, on different modifications of Hill estimators. Regarding the estimation of the tail index (a positive EVI) in dependent structures, I refer a unique article by Gomes and Miranda, [238].…”