Dependence on Tail Copula

Abstract

In real-world scenarios, we encounter non-exchangeable dependence structures. Our primary focus is on identifying and quantifying non-exchangeability in the tails of joint distributions. The findings and methodologies presented in this study are particularly valuable for modeling bivariate dependence, especially in fields where understanding dependence patterns in the tails is crucial, such as quantitative finance, quantitative risk management, and econometrics. To grasp the intricate relationship between the strength of dependence and various types of margins, we explore three fundamental tail behavior patterns for univariate margins. Capitalizing on the probabilistic features of tail non-exchangeability structures, we introduce graphical techniques and statistical tests designed for analyzing data that may manifest non-exchangeability in the joint tail. The effectiveness of the proposed approaches is illustrated through a simulation study and a practical example.

Measuring Asymmetric Tails Under Copula Distributions

“…They used these approximations in exchangeable copulas. In our paper, we are using the same method after transforming a copula into a non-exchangeable structure [33].…”

“…To contextualize, this probability is immensely smaller than the chance of selecting a specific atom from the entirety of atoms in the observable universe, estimated to be 10 8 0! [33].…”