Risk measure estimation for $\beta$-mixing time series and applications

TL;DR

This paper develops bias-corrected tail estimators for $eta$-mixing time series within extreme value theory, demonstrating improved estimation of extreme quantiles through simulations and real data applications.

Contribution

It introduces a novel bias-correction method combining two estimators for the extreme value index in $eta$-mixing sequences, enhancing tail estimation accuracy.

Findings

Estimator performs well in simulations compared to existing methods.

Asymptotic variance computed for specific models.

Applied to finance and environmental datasets with successful results.

Abstract

In this paper, we discuss the application of extreme value theory in the context of stationary $\beta$-mixing sequences that belong to the Fr\'echet domain of attraction. In particular, we propose a methodology to construct bias-corrected tail estimators. Our approach is based on the combination of two estimators for the extreme value index to cancel the bias. The resulting estimator is used to estimate an extreme quantile. In a simulation study, we outline the performance of our proposals that we compare to alternative estimators recently introduced in the literature. Also, we compute the asymptotic variance in specific examples when possible. Our methodology is applied to two datasets on finance and environment.