Interval estimation for bivariate t-copulas via Kendall’s tau

Copula models have been popular in risk management. Due to the properties of asymptotic dependence and easy simulation, the t-copula has often been employed in practice. A computationally simple estimation procedure for the t-copula is to first estimate the linear correlation via Kendall’s tau estimator and then to estimate the parameter of the number of degrees of freedom by maximizing the pseudo likelihood function. In this paper, we derive the asymptotic limit of this two-step estimator which results in a complicated asymptotic covariance matrix. Further, we propose jackknife empirical likelihood methods to construct confidence intervals/regions for the parameters and the tail dependence coefficient without estimating any additional quantities. A simulation study shows that the proposed methods perform well in finite sample. Key-words: Jackknife empirical likelihood, Kendall’s tau, t-copula ∗School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA. Email address: [email protected] †Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada. Email address: [email protected]