No abstract

This paper defines two distribution free goodness-of-fit test statistics for copulas. It states their asymptotic distributions under some composite parametric assumptions in an independent identically distributed framework. A short simulation study is provided to assess their power performances.

We consider a nonparametric method to estimate copulas, i.e. functions linking joint distributions to their univariate margins. We derive the asymptotic properties of kernel estimators of copulas and their derivatives in the context of a multivariate stationary process satisfactory strong mixing conditions. Monte Carlo results are reported for a stationary vector autoregressive process of order one with Gaussian innovations. An empirical illustration containing a comparison with the independent, comotonic and Gaussian copulas is given for European and US stock index returns.

Existing simulation-based estimation methods are either general purpose but asymptotically inefficient or asymptotically efficient but only suitable for restricted classes of models+ This paper studies a simulated maximum likelihood method that rests on estimating the likelihood nonparametrically on a simulated sample+ We prove that this method, which can be used on very general models, is consistent and asymptotically efficient for static models+ We then propose an extension to dynamic models and give some Monte-Carlo simulation results on a dynamic Tobit model+