Hidden Regular Variation under Full and Strong Asymptotic Dependence

TL;DR

This paper explores hidden regular variation in bivariate heavy-tailed data under full and strong asymptotic dependence, improving risk estimation by identifying dependence structures often missed by standard methods.

Contribution

It introduces the concepts of full and strong asymptotic dependence and discusses hidden regular variation, enhancing risk analysis in dependent heavy-tailed data.

Findings

Hidden regular variation can reveal risks underestimated by traditional methods.

Analysis of real and simulated data demonstrates detection of dependence structures.

Improved risk estimation accuracy in heavy-tailed dependent data.

Abstract

Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the data tends to concentrate along particular directions and does not cover the full space. This is observed in various data sets from finance, insurance, network traffic, social networks, etc. In this paper we discuss the notions of full and strong asymptotic dependence for bivariate data along with the idea of hidden regular variation in these cases. In a risk analysis setting, this leads to improved risk estimation accuracy when regular methods provide a zero estimate of risk. Analyses of both real and simulated data sets illustrate concepts of generation and detection of such models.