Functional Tail Dependence Coefficients for Copula

• Activity Number: 519 - SPEED: Methodological Advances in Time Series: BandE Speed Session, Part 2
• Type: Contributed
• Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 11:15 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Keying Ye* and Zhiruo Liu and Donald Lien
• Companies: University of Texas at San Antonio and University of Texas at San Antonio and University of Texas at San Antonio
• Keywords: Tail dependence coefficients; Copula; Associations between variables; Functional tail dependence

Abstract

Researchers and practitioners are interested in the associations between variables at extreme values in which large amount of profits or losses in financial industry are considered. Sibuya (1960) proposed a conditional dependence structure, called tail dependence coefficient, to measure the asymptotic dependency between variables. This coefficient has become a standard measurement of associations between variables at extreme values.

In this talk, we propose a functional tail dependence structure between two variables at their extremities in the sense that the rates approaching to extremities are functionally different. We obtain definite solutions of such proposed tail dependence coefficients for six commonly used copulas under mild assumptions. In addition, empirical studies are carried out for financial data.