Multivariate GARCH models: software choice and estimation issues

The development of multivariate generalized autoregressive conditionally heteroscedastic (MGARCH) models from the original univariate specifications represented a major step forward in the modelling of time series. MGARCH models permit time-varying conditional covariances as well as variances, and the former quantity can be of substantial practical use for both modelling and forecasting, especially in finance. For example, applications to the calculation of time-varying hedge ratios, value at risk estimation, and portfolio construction have been developed.Whilst a number of reviews have investigated the accuracy, ease of use, availability of documentation and other attributes of the software available for the estimation of univariate GARCH models (see, for example, Brooks, 1997; McCullough and Renfro, 1999; Brooks et al., 2001), to our knowledge none has yet conducted a comparative study of the usefulness of thevarious packages available for multivariate GARCH model estimation, in spite of the empirical importance of this class of models. Brooks et al. (2001) employed the FCP (Fiorentini et al., 1996) benchmark for evaluating the accuracy of the parameter estimates in the context of univariate GARCH models and stressed the importance of the development of benchmarks for other non-linear models, including others inthe GARCH class. However, there are currently no benchmarks yet developed for multivariate GARCH models. Therefore it will not be possible to write in terms of one package being moreor less accurate than another; rather, all that can be done is to point out the differences in results that can arise if a different package is employed. In order to determine how large are the potential practical implications of any differences in coefficient estimates, we employ the data used by Brooks et al. (2002) in their estimation of optimal hedge ratios (OHRs).