Tail dependence of skew t-copulas

ABSTRACT

We examine tail behavior of skew t-copula in the bivariate case. The tail dependence coefficient is calculated for different skewing parameter values and compared with the corresponding coefficient for the t-copula. It is shown that depending on skewing parameter values, the tail dependence coefficient can differ considerably from the tail dependence of the t-copula. The speed of convergence of the estimator of tail dependence coefficient to its theoretical value is examined in a simulation experiment. Method of moments and maximum likelihood method are compared by simulation either. In the considered cases, maximum likelihood method converged faster to the theoretical value.

KEYWORDS:

• Simulation
• Skew normal copula
• Skew normal distribution
• Skew t-copula
• Skew t-distribution
• Tail dependence

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H20
• 62F12
• 62E20

Funding

T. Kollo and M. Valge are grateful for financial support from project IUT34-5 and Estonian Science Foundation through the grant GMTMS9127.