Statistical analysis for stationary time series at extreme levels: new estimators for the limiting cluster size distribution

TL;DR

This paper introduces new estimators for the limiting cluster size distribution in stationary time series at extreme levels, demonstrating their theoretical properties and superior performance through simulations.

Contribution

It proposes novel estimators based on blocks declustering that depend on only one parameter and compares their effectiveness to existing methods.

Findings

Sliding blocks estimators outperform disjoint blocks versions.

Estimators depend on a single unknown parameter.

Simulation results show improved accuracy over competitors.

Abstract

A measure of primal importance for capturing the serial dependence of a stationary time series at extreme levels is provided by the limiting cluster size distribution. New estimators based on a blocks declustering scheme are proposed and analyzed both theoretically and by means of a large-scale simulation study. A sliding blocks version of the estimators is shown to outperform a disjoint blocks version. In contrast to some competitors from the literature, the estimators only depend on one unknown parameter to be chosen by the statistician.