ON THE PARAMETRIZATION OF MULTIVARIATE GARCH MODELS

Wolfgang Scherrer and Eva Ribarits

Econometric Theory, 2007, vol. 23, issue 03, pages 464-484

Abstract: This paper deals with issues of structure and parametrization of VECH models proposed in Bollerslev, Engle, and Wooldridge (1988) and Baba, Engle, Kraft, and Kroner (BEKK) models. Both general models and also restricted versions such as the widely used diagonal VECH (DVECH) and factor generalized autoregressive conditional heteroskedastic (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, Econometric Theory 11, 122 150) 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.This research was supported by the project P17065 Identification of multivariate dynamic systems with a focus on dimension reduction of the Austrian Science Foundation (FWF).

Date: 2007
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