Pair Copula Constructions of Multivariate Copulas and Their Applications

• Activity Number: 502
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Claudia Czado*+
• Companies: Technische Universität München
• Keywords: multivariate copulas ; pair copula constructions ; vines ; dependence ; MCMC ; multivariate time series

Abstract

Pair copula constructions (PCC) allow to construct very flexible multivariate distributions. These are characterized by a sequence of trees called a vine structure, bi-variate copula families and marginal distributions (see Kurowicka and Cooke (2006, Wiley\& Sons) and Kurowicka and Joe (2011, World Scientific)). Two studied subclasses are C- and D-vines. The multivariate Gauss and t-distribution are special cases. This class is very useful for modeling of multivariate data in economics and finance, since it can capture non symmetric and different tail dependencies (see Aas et.al (2009, IME) and Fischer at el (2010, QF)). I will introduce PCC models and discuss different estimating methods including maximum likelihood and Bayesian inference (see Min and Czado (2010, JFES)). Since the class of PCC models is very large model selection is vital. In Min und Czado (2010, CJS) and Smith et. al (2010, JASA) two MCMC methods are developed to detect conditional independences in a given D-vine, which I will discuss. Finally I will introduce a first approach to find appropriate regular vines structures. Methods will be illustrated by applications to financial times series.