Tail Order and Intermediate Tail Dependence of Multivariate Copulas

• Activity Number: 517
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Lei Hua*+ and Harry Joe
• Companies: The University of British Columbia and The University of British Columbia
• Keywords: Archimedean copula ; Laplace transform ; tail asymmetry ; regular variation

Abstract

In order to study copula families that have different tail rates and asymmetry than multivariate Gaussian and t copulas, we use a coefficient of tail order. Strong tail dependence has been important in applications where copulas are used for inference on tail probabilities, but the tail order can also cover intermediate tail dependence. For multivariate Archimedean copulas and other copula constructions based on Laplace transforms, we relate the tail order to the asymptotic behavior of Laplace transforms at 0 and infinity, and to the tails of the density of the mixing random variable. Some further properties of tail orders that are studied include tail relationships between a copula function and its density, and between a copula and its margins.