A Multivariate Markov-Switching GARCH Model with Copula-Distributed Innovations

Abstract

In order to improve the dynamic assessment of financial market interdependencies, we develop a new Markov switching approach to multivariate volatility modelling. More specific, we take advantage of the flexible copula multivariate GARCH model of Lee and Long (2009), and allow state dependence with regard to the dependence structure governed by copula functions. We show some asymptotic features of the new model and motivate a two-step approach to maximum likelihood (ML)-estimation. As an empirical illustration, we consider a bivariate series comprising the returns of a high-yield equity index (MSCI World Developed Markets) and a traditional safe-haven asset (gold), and compare the goodness-of-fit of the new model with existing multivariate GARCH approaches. The new model offers advantages when it comes to detect and depict flows between financial assets in order to reduce portfolio risks in extreme market situations. We find that the suggested Markov switching generalization of the copula-MGARCH model of Lee and Long (2009) benefits from capturing structural changes in the non-linear dependence patterns, and helps to uncover flight-to-safety effects in times of economic turmoil.