Three-Stage Semi-Parametric Estimation of T-Copulas : Asymptotics, Finite-Sample Properties and Computational Aspects

Genest, C., Ghoudi, K., Rivest, L.P. (1995) proposed a two-stage semi-parametric estimation procedure for a broad class of copulas satisfying minimal regularity conditions. 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. The asymptotic properties of this methodology are developed and its finite-sample behavior are examined via simulations. The pros and cons of this methodology are then analyzed in terms of numerical convergence and positive definiteness of the estimated T-copula correlation matrix