Measuring Extreme Tail Association

2026-03-13

AI Summary

This study addresses the limitation of existing extremal dependence measures, which are predominantly symmetric and thus unable to capture directional effects in tail associations. To overcome this, the authors propose a rank-based Extreme Tail Asymmetry (ETA) measure that quantifies the asymmetric influence of one variable on another within extreme tail regions of bivariate distributions. They develop a statistical test based on the multiplier bootstrap procedure, introducing—for the first time—an asymmetric metric capable of discerning tail directionality, thereby offering a novel perspective for causal inference under extreme conditions. The proposed estimator is shown to be consistent and asymptotically normal, with high computational efficiency. Empirical validation on cryptocurrency price data exhibiting extreme volatility demonstrates both the method’s effectiveness and favorable statistical properties.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Simultaneous occurrences of extreme events need not imply symmetric or reciprocal tail dependence. However, most existing measures of extremal dependence are inherently symmetric and hence often fail to capture directional influence in tail association. We introduce a rank-based measure of Extreme Tail Association (ETA) for bivariate data quantifying such directional influence of one variable on another in extreme tail regions. The proposed estimator is easily computable, consistent with its population counterpart, and asymptotically normal under mild conditions, allowing for statistical inference. We further develop a formal test for asymmetry in tail association based on a multiplier bootstrap procedure. The practical relevance of the methodology is illustrated using data on extreme price movements in major cryptocurrencies. Beyond providing a flexible tool for extremal association, the proposed framework offers a substantive argument for investigating causal relationships in extreme scenarios.

Problem

• extreme tail association
• asymmetric dependence
• directional influence
• extremal dependence
• tail dependence

Innovation

• Extreme Tail Association
• directional tail dependence
• asymmetry test
• rank-based estimator
• multiplier bootstrap