Modelling the Dynamic Dependence Structure in Multivariate Financial Time Series

. The dependence structure in multivariate financial time series is of great importance in portfolio management. By studying daily return histories of 17 exchange‐traded index funds, we identify important features of the data, and we propose two new models to capture these features. The first is an extension of the multivariate BEKK (Baba, Engle, Kraft, Kroner) model, which includes a multivariate t‐type error distribution with different degrees of freedom. We demonstrate that this error distribution is able to accommodate different levels of heavy‐tailed behaviour and thus provides a better fit than models based on a multivariate t‐with a common degree of freedom. The second model is copula based, and can be regarded as an extension of the standard and the generalized dynamic conditional correlation model [Engle, Journal of Business and Economics Statistics (2002) Vol. 17, 425–446; Cappiello et al. (2003) Working paper, UCSD] to a Student copula. Model comparison is carried out using criteria including the Akaike information criteria and Bayesian information criteria. We also evaluate the two models from an asset‐allocation perspective using a three‐asset portfolio as an example, constructing optimal portfolios based on the Markowitz theory. Our results indicate that, for our data, the proposed models both outperform the standard BEKK model, with the copula model performing better than the extension of the BEKK model.