In this paper we propose a new MGARCH model, namely, the C-MGARCH model. The
C-MGARCH model includes a conventional MGARCH model as a special case. The CMGARCH
model is to exploit the fact that the uncorrelated errors are not necessarily independent.
The C-MGARCH model permits modeling the conditional covariance for the
non-elliptically distributed financial returns, and at the same time separately modeling the
dependence structure beyond the conditional covariance. While we have considered here
only a bivariate system, the extension to a higher dimension is straightforward. We compare
the C-MGARCH models with the corresponding MGARCH models using the three financial
data sets — a pair of the U.S. equity indices and two pairs of the foreign exchange rates.
The empirical results from the in-sample and out-of-sample analysis clearly demonstrate the
advantages of the new model.