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ON THE RELATION BETWEEN THE VEC AND BEKK MULTIVARIATE GARCH MODELS

Published online by Cambridge University Press:  04 April 2008

Robert Stelzer
Robert Stelzer*
Affiliation:
Munich University of Technology
*
Address correspondence to Robert Stelzer, Centre for Mathematical Sciences, Munich University of Technology, Boltzmannstraße 3, D-85747 Garching, Germany; e-mail: rstelzer@ma.tum.de.
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Abstract

The question of which multivariate generalized autoregressive conditionally heteroskedastic (GARCH) models in the vec form are representable in the BEKK form is addressed. Using results from linear algebra, it is established that all vec models not representable in the simplest BEKK form contain matrices as parameters that map the vectorized positive semidefinite matrices into a strict subset of themselves. Moreover, a general result from linear algebra is presented implying that in dimension two the models are equivalent, and in dimension three a simple analytically tractable example for a vec model having no BEKK representation is given.

Information

Type
Notes and Problems
Information
Econometric Theory , Volume 24 , Issue 4 , August 2008 , pp. 1131 - 1136
Copyright
Copyright © Cambridge University Press 2008

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