Maximum likelihood estimation of mixed C-vines with application to exchange rates

Abstract

Multivariate copulas are commonly used in economics, finance and risk management. They allow for very flexible dependency structures, even though they are applied to transformed financial data after marginal time dependencies are removed. This is necessary to facilitate statistical parameter estimation. In this paper we consider a very flexible class of mixed C-vines, which allows the variables to be ordered according to their influence. Vines are built from bivariate copulas only and the term ‘mixed’ refers to allowing the pair-copula family to be chosen individually for each term. In addition there are many C-vine structure specifications possible and therefore we propose a novel data driven sequential selection procedure, which selects both the C-vine structure and its attached pair-copula families with parameters. After the model selection maximum likelihood (ML) estimation of the parameters is facilitated using the sequential estimates as starting values. An extensive simulation study shows a satisfactory performance of ML estimates in small samples. Finally an application involving US-exchange rates demonstrates the need for mixed C-vine models.