Directional Dependence of Extreme Events

TL;DR

This paper proposes a new measure for quantifying asymmetric directional dependence of extreme events between variables, useful for understanding causality in extreme-value analysis.

Contribution

It introduces a novel measure based on conditional tail expectations to capture asymmetric tail dependence and explores its theoretical properties and applications.

Findings

The measure effectively captures asymmetric tail dependence in simulations.

Application to oceanographic data reveals dominant directions of extremal influence.

The approach can be used to detect causal effects in extreme events.

Abstract

This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of rank-transformed variables, thereby quantifying the behavior of one variable when the other takes extreme values. We investigate the theoretical asymptotic behavior of the associated estimator. The effectiveness of the approach is demonstrated through an extensive simulation study. In addition, we discuss the use of the proposed coefficient for the detection of causal effects in extreme events. Finally, we apply the method to an oceanographic dataset, where the results highlight the strong asymmetric nature of extreme events and identify the dominant directions of extremal influence among key oceanographic variables. As a directional measure of tail dependence, our approach provides a natural tool for exploring causal-effect relationships in extreme-value settings.