Method of moments estimators for the extremal index of a stationary time series

TL;DR

This paper introduces new rank-based method of moments estimators for the extremal index of stationary time series, showing improved performance especially when the extremal index is close to one.

Contribution

The paper proposes novel rank-based estimators for the extremal index using the method of moments, with theoretical analysis and empirical validation demonstrating their advantages.

Findings

Estimators perform well in theoretical analysis.

Empirical results show superiority for $ heta o 1$ scenarios.

Outperforms recent competitors in specific cases.

Abstract

The extremal index $\theta$, a number in the interval $[0,1]$, is known to be a measure of primal importance for analyzing the extremes of a stationary time series. New rank-based estimators for $\theta$ are proposed which rely on the construction of approximate samples from the exponential distribution with parameter $\theta$ that is then to be fitted via the method of moments. The new estimators are analyzed both theoretically as well as empirically through a large-scale simulation study. In specific scenarios, in particular for time series models with $\theta \approx 1$, they are found to be superior to recent competitors from the literature.