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      Stationarity and Geometric Ergodicity of BEKK Multivariate GARCH Models

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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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          Generalized autoregressive conditional heteroskedasticity

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            Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation

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              Multivariate GARCH models: a survey

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                Author and article information

                Journal
                01 June 2011
                Article
                10.1016/j.spa.2011.06.001
                1106.0165

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                60J05, 60B99, 62M10, 91G70
                Stochastic Processes and their Applications 2011, Vol. 121, No. 10, 2331-2360
                version to appear in Stochastic Processes and their Applications, 2011; http://www.sciencedirect.com/science/article/pii/S0304414911001372
                math.PR

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