Selecting and estimating regular vine copulae and application to financial returns

TL;DR

This paper introduces a new method for selecting and estimating regular vine copulae, enabling flexible modeling of complex dependencies in high-dimensional financial data, with applications to international financial indices.

Contribution

It presents a novel automated model selection and estimation technique for regular vine copulae based on graph theory, expanding their applicability to larger dimensions.

Findings

Effective modeling of complex dependencies in 16-dimensional financial data

Insights into dependence structures among international financial indices

Demonstrated robustness during financial crisis periods

Abstract

Regular vine distributions which constitute a flexible class of multivariate dependence models are discussed. Since multivariate copulae constructed through pair-copula decompositions were introduced to the statistical community, interest in these models has been growing steadily and they are finding successful applications in various fields. Research so far has however been concentrating on so-called canonical and D-vine copulae, which are more restrictive cases of regular vine copulae. It is shown how to evaluate the density of arbitrary regular vine specifications. This opens the vine copula methodology to the flexible modeling of complex dependencies even in larger dimensions. In this regard, a new automated model selection and estimation technique based on graph theoretical considerations is presented. This comprehensive search strategy is evaluated in a large simulation study and applied to a 16-dimensional financial data set of international equity, fixed income and commodity indices which were observed over the last decade, in particular during the recent financial crisis. The analysis provides economically well interpretable results and interesting insights into the dependence structure among these indices.