Copula Density Estimation by Total Variation Penalized Likelihood

Abstract

Copulas are full measures of dependence among random variables. They are increasingly popular among academics and practitioners in financial econometrics for modeling comovements between markets, risk factors, and other relevant variables. A copula’s hidden dependence structure that couples a joint distribution with its marginals makes a parametric copula non-trivial. An approach to bivariate copula density estimation is introduced that is based on a penalized likelihood with a total variation penalty term. Adaptive choice of the amount of egularization is based on approximate Bayesian Information Criterion (BIC) type scores. Performance are evaluated through the Monte Carlo simulation.

Keywords: Copula, Dependence modeling, Density estimation, Total variation