Partial Tail-Correlation Coefficient Applied to Extremal-Network Learning

TL;DR

This paper introduces the partial tail-correlation coefficient (PTCC), a new measure for extremal dependence that enables efficient learning of extremal network structures with minimal assumptions, demonstrated on environmental and financial data.

Contribution

The paper presents the PTCC, a novel extremal dependence measure based on multivariate regular variation, facilitating exploratory extremal network learning with classical inference methods.

Findings

PTCC effectively identifies extremal relationships in data.

Application to river discharges reveals meaningful extremal structures.

Application to currency data uncovers interpretable extremal networks.

Abstract

We propose a novel extremal dependence measure called the partial tail-correlation coefficient (PTCC), in analogy to the partial correlation coefficient in classical multivariate analysis. The construction of our new coefficient is based on the framework of multivariate regular variation and transformed-linear algebra operations. We show how this coefficient allows identifying pairs of variables that have partially uncorrelated tails given the other variables in a random vector. Unlike other recently introduced conditional independence frameworks for extremes, our approach requires minimal modeling assumptions and can thus be used in exploratory analyses to learn the structure of extremal graphical models. Similarly to traditional Gaussian graphical models where edges correspond to the non-zero entries of the precision matrix, we can exploit classical inference methods for high-dimensional data, such as the graphical LASSO with Laplacian spectral constraints, to efficiently learn the extremal network structure via the PTCC. We apply our new method to study extreme risk networks in two different datasets (extreme river discharges and historical global currency exchange data) and show that we can extract meaningful extremal structures with meaningful domain-specific interpretations.