Truncated regular vines in high dimensions with application to financial data

TLDR

Regular vine copulas use only bivariate copulas and offer flexible high‑dimensional dependency modeling, but their flexibility leads to exponentially increasing complexity as dimensionality grows. The study proposes using statistical model selection to truncate or simplify regular vine copulas to mitigate this complexity. The authors simplify canonical vine copulas with a multivariate copula approach, validating the methods through extensive simulations and a 19‑dimensional financial dataset. The validation demonstrates that the truncated or simplified vine models perform well in simulations and effectively capture dependencies in the 19‑dimensional financial data. © 2012 Statistical Society of Canada, The Canadian Journal of Statistics 40:68–85.

Abstract

Abstract Using only bivariate copulas as building blocks, regular vine copulas constitute a flexible class of high‐dimensional dependency models. However, the flexibility comes along with an exponentially increasing complexity in larger dimensions. In order to counteract this problem, we propose using statistical model selection techniques to either truncate or simplify a regular vine copula. As a special case, we consider the simplification of a canonical vine copula using a multivariate copula as previously treated by Heinen & Valdesogo ( 2009 ) and Valdesogo ( 2009 ). We validate the proposed approaches by extensive simulation studies and use them to investigate a 19‐dimensional financial data set of Norwegian and international market variables. The Canadian Journal of Statistics 40: 68–85; 2012 © 2012 Statistical Society of Canada