Stationarity and geometric ergodicity of BEKK multivariate GARCH models
Copyright policy )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 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.
version to appear in Stochastic Processes and their Applications, 2011; http://www.sciencedirect.com/science/article/pii/S0304414911001372
- University of Montpellier France
- Technical University of Munich Germany
- University of Ulm Germany
- University of Montpellier France
- TUM Institute for Advanced Study
Stationarity, Statistics and Probability, Geometric ergodicity, Foster–Lyapunov drift condition, Applied Mathematics, Probability (math.PR), β-mixing, Probability theory on algebraic and topological structures, Harris recurrence, Time series, auto-correlation, regression, etc. in statistics (GARCH), Foster-Lyapunov drift condition, Discrete-time Markov processes on general state spaces, Modelling and Simulation, FOS: Mathematics, Multivariate GARCH, Stochastic volatility, stochastic volatility, \(\beta\)-mixing, 60J05, 60B99, 62M10, 91G70, Mathematics - Probability, Statistical methods; risk measures
Stationarity, Statistics and Probability, Geometric ergodicity, Foster–Lyapunov drift condition, Applied Mathematics, Probability (math.PR), β-mixing, Probability theory on algebraic and topological structures, Harris recurrence, Time series, auto-correlation, regression, etc. in statistics (GARCH), Foster-Lyapunov drift condition, Discrete-time Markov processes on general state spaces, Modelling and Simulation, FOS: Mathematics, Multivariate GARCH, Stochastic volatility, stochastic volatility, \(\beta\)-mixing, 60J05, 60B99, 62M10, 91G70, Mathematics - Probability, Statistical methods; risk measures
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