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W. Scherrer, E. Ribarits:
"On the Parametrization of Multivariate GARCH Models";
Econometric Theory, 23 (2007), 464 - 484.

This paper deals with issues of structure and parametrization of VECH and BEKK models. Both general models as well as restricted versions such as the widely used diagonal VECH (DVECH) and factor GARCH (F-GARCH) models are discussed. A simple algorithm is presented that checks whether a given VECH model may be cast as a BEKK model. It is shown that in the bivariate case BEKK models are as general as VECH models. In higher dimensional cases however, VECH models allow for more flexibility. In addition, a parametrization for a generic, i.e. open and dense, class of BEKK models is given and the frequently cited parametrization by (Engle and Kroner, 1995) is analyzed. Two shortcomings of the latter are pointed out. Finally, parametrizations for BEKK(p, q, K) models with K ≤ n, including DVECH, F-GARCH and a generalization of the latter, are discussed.