Copula estimation through wavelets

Abstract

Recently some nonparametric estimation procedures have been proposed using kernels and wavelets to estimate the copula function. In this context, knowing that a copula function can be expanded in a wavelet basis, we propose a new nonparametric copula estimation procedure through wavelets for independent data and times series under an $\alpha $-mixing condition. The main feature of this estimator is that we make no assumptions on the data distribution and there is no need to use ARMA–GARCH modelling before estimating the copula. Convergence rates for the estimator were computed, showing the estimator consistency. Some simulation studies are presented, as well as analysis of real data sets.