NONPARAMETRIC ESTIMATION OF COPULAS FOR TIME SERIES

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 es-timators 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 illus-tration containing a comparison with the independent, comotonic and Gaussian copulas is given for European and US stock index returns