Semiparametric Dynamic Max-Copula Model for Multivariate Time Series

Abstract

SummaryThe paper presents a novel non-linear framework for the construction of flexible multivariate dependence structure (i.e. copulas) from existing copulas based on a straightforward ‘pairwise max-’rule. The newly constructed max-copula has a closed form and has strong interpretability. Compared with the classical ‘linear symmetric’ mixture copula, the max-copula can be viewed as a ‘non-linear asymmetric’ framework. It is capable of modelling asymmetric dependence and joint tail behaviour while also offering good performance in non-extremal behaviour modelling. Max-copulas that are based on single-factor and block factor models are developed to offer parsimonious modelling for structured dependence, especially in high dimensional applications. Combined with semiparametric time series models, the max-copula can be used to develop flexible and accurate models for multivariate time series. A new semiparametric composite maximum likelihood method is proposed for parameter estimation, where the consistency and asymptotic normality of estimators are established. The flexibility of the max-copula and the accuracy of the proposed estimation procedure are illustrated through extensive numerical experiments. Real data applications in value-at-risk estimation and portfolio optimization for financial risk management demonstrate the max-copula's promising ability to capture accurately joint movements of high dimensional multivariate stock returns under both normal and crisis regimes of the financial market.