181 – Finance, Heteroscedasticity, and Copulas
On Bivariate Tail Non-Exchangeability
Paramahansa Pramanik
Northern Illinois University
Lei Hua
Northern Illinois University
Alan Polansky
Northern Illinois University
The study is about identifying existence of non-exchangeability in the joint distributional tails, and how to quantify the degree of such tail non-exchangeability. The approaches proposed benefit bivariate dependence modeling when tail dependence patterns are important. We propose to use conditional expectations as the basis quantities. Then for random variables X and Y, the departure between tail behavior of E[X|Y> t] and E[Y|X> t], or E[X|Y= t] and E[Y|X= t], becomes sensible in detecting tail non-exchangeability. We use a bivariate copula to model dependency between X and Y. Various devices of generating non-exchangeable copulas as well as three major tail behaviors for univariate margins are studied for the interaction between the departure of those conditional expectations and the non-exchangeable dependence together with various types of margins. Based on the probabilistic properties of the tail non-exchangeability structures, we develop graphical approaches and statistical tests for analyzing dataset that may have non-exchangeability in the joint tail. Simulation study and empirical study are then conducted to demonstrate the usefulness of the proposed approaches.