Measuring Extreme Tail Association

TL;DR

This paper introduces a new rank-based measure for directional tail dependence in bivariate data, enabling better understanding of extreme event influence and causal inference in extreme scenarios.

Contribution

It proposes a novel asymmetric measure of extremal dependence, along with an estimator, inference procedures, and a test for tail asymmetry, applicable to real-world data.

Findings

The estimator is consistent and asymptotically normal.

The method effectively detects directional influence in extreme events.

Application to cryptocurrency data demonstrates practical utility.

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.