Stationarity and geometric ergodicity of BEKK multivariate GARCH models

Stationarity and Geometric Ergodicity of BEKK Multivariate GARCH Models

Conditions for the existence of strictly stationary multivariate GARCH processes in the so-called BEKK parametrisation, which is the most general form of multivariate GARCH processes typically used in applications, and for their geometric ergodicity are obtained. The conditions are that the driving noise is absolutely continuous with respect to the Lebesgue measure and zero is in the interior o...

Do We Really Need Both BEKK and DCC? A Tale of Two Multivariate GARCH Models

Discussion Papers are a series of manuscripts in their draft form. They are not intended for circulation or distribution except as indicated by the author. For that reason Discussion Papers may not be reproduced or distributed without the written consent of the author. for financial support. This is an abridged and revised version of a paper entitled " Do we really need both BEKK and DCC? A tal...

On the Relation Between the vec and BEKK Multivariate GARCH Models

The question which multivariate 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 which map the vectorised positive semi-definite matrices into a strict subset of themselves. Moreover, a general result from linear algebra...

Stationarity and geometric ergodicity of a class of nonlinear ARCH models

Semiparametric Multivariate Garch Models

Estimation of multivariate GARCH models is usually carried out by quasi maximum likelihood (QMLE), for which recently consistency and asymptotic normality have been proven under quite general conditions. However, there are to date no results on the efficiency loss of QMLE if the true innovation distribution is not multinormal. We investigate this issue by suggesting a nonparametric estimation o...