Robust fits for copula models

Abstract

In this paper we propose and compare two different methodologies for fitting copulas robustly. The first proposal consists of a robustification of the maximum likelihood method, where points previously identified as outliers by a high breakdown point covariance matrix estimator are downweighted in a maximum likelihood optimization procedure. The second proposal obtains robust estimates by minimizing selected empirical copula based goodness of fit statistics. We show through simulations that the proposed robust estimators are able to capture the correct strength of dependence of the data, providing more accurate estimates of copula based dependence measures such as the tail dependence coefficient. The experiments considered several ε- contaminated copula models, for varying proportions ε of contaminating points. Another result in this paper is the finite sample distribution of some selected empirical copula based statistics and corresponding tables for testing and selecting the best copula fit.