Stationarity and geometric ergodicity of BEKK multivariate GARCH models |
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| Authors: | Farid Boussama Robert Stelzer |
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| Affiliation: | a Département Informatique et Mathématique, Université Montpellier 1, 39 Rue de l’Université, 34000 Montpellier, Franceb TUM Institute for Advanced Study & Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, D-85748 Garching, Germanyc Institute of Mathematical Finance, Ulm University, Helmholtzstraße 18, D-89081 Ulm, Germany |
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| Abstract: | 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 of its support and that a certain matrix built from the GARCH coefficients has spectral radius smaller than one.To establish the results, semi-polynomial Markov chains are defined and analysed using algebraic geometry. |
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| Keywords: | primary, 60J05 secondary, 60B99, 62M10, 91G70 |
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