Cluster based inference for extremes of time series

TL;DR

This paper presents a novel estimator for the spectral tail process of regularly varying time series, utilizing a projection technique and invariance property, with proven asymptotic normality and improved stability in simulations.

Contribution

Introduces a new spectral tail process estimator based on invariance and projection, with theoretical and empirical validation.

Findings

Estimator exhibits uniform asymptotic normality

Performs more stably than previous methods in simulations

Works for known and unknown regular variation index

Abstract

We introduce a new type of estimator for the spectral tail process of a regularly varying time series. The approach is based on a characterizing invariance property of the spectral tail process, which is incorporated into the new estimator via a projection technique. We show uniform asymptotic normality of this estimator, both in the case of known and of unknown index of regular variation. In a simulation study the new procedure shows a more stable performance than previously proposed estimators.