Three-stage semi-parametric estimation of T-copulas: Asymptotics, finite-sample properties and computational aspects

Genest et al. (1995) proposed a two-stages semi-parametric estimation procedure for bivariate Archimedean copulas. A three stage semi-parametric estimation method based on Kendall’s tau has been recently proposed in the financial literature to estimate the Student’s T copula, too. Its major advantage is to allow for greater computational tractability when dealing with high dimensional issues, where two-stage procedures are no more a viable choice. We develop the asymptotic properties of this methodology and we examine its finite-sample behavior via simulations. We then analyze the pros and cons of this methodology in terms of numerical convergence and positive definiteness of the estimated T-copula correlation matrix.