Intermediate Tail Dependence: A Review and Some New Results

TL;DR

This paper reviews the concept of intermediate tail dependence in dependence modeling, covering elliptical, extreme value, and Archimedean copulas, and introduces new results including conditions for scale mixture models to exhibit intermediate tail dependence.

Contribution

It provides a comprehensive review of intermediate tail dependence and introduces new conditions for scale mixture models to generate such dependence structures.

Findings

Conditions for scale mixture models to exhibit intermediate tail dependence

Review of intermediate tail dependence in elliptical, extreme value, and Archimedean copulas

New methods for simulating copulas with intermediate tail dependence

Abstract

The concept of intermediate tail dependence is useful if one wants to quantify the degree of positive dependence in the tails when there is no strong evidence of presence of the usual tail dependence. We first review existing studies on intermediate tail dependence, and then we report new results to supplement the review. Intermediate tail dependence for elliptical, extreme value and Archimedean copulas are reviewed and further studied, respectively. For Archimedean copulas, we not only consider the frailty model but also the recently studied scale mixture model; for the latter, conditions leading to upper intermediate tail dependence are presented, and it provides a useful way to simulate copulas with desirable intermediate tail dependence structures.