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

Abstract

The extremal index θ, 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 rankbased estimators for θ are proposed which rely on the construction of approximate samples from the exponential distribution with parameter θ 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 θ ≈ 1, they are found to be superior to recent competitors from the literature.