Stationarity and geometric ergodicity of BEKK multivariate GARCH models
By Farid Boussama, F. Fuchs, Robert Stelzer. 2011
100 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Finance
View Paper: https://www.semanticscholar.org/paper/f3fccddf8042e418f02d5a1098079b05fc03d22f
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Citations in the corpus
- MGARCH models: Trade-off between feasibility and flexibility (2018, background): “The conditions for strict stationarity and geometric ergodicity can be found in Boussama et al. (2011).”
- Multivariate Variance Targeting in the BEKK-GARCH Model (2014, unknown): “A.3 Proof of Proposition 4.1 Notice that vec[C (θ)] = [Id2 − (A⊗ A)− (B ⊗B)] γ.”
- Estimating multivariate volatility models equation by equation (2016, background): “By Boussama et al. (2011) and Aielli (2013), the conditions of theorem 4 ensure the existence of a strictly stationary, non-anticipative and ergodic solution .vech.”
- Dynamic Conditional Correlation: On Properties and Estimation (2013, unknown): “As for the stationarity of the correlation/standardized return process, explicit conditions are derived from a recent result by Boussama, Fuchs, and Stelzer (2011) on the stationarity of linear MGARCH processes.”
- Modelling matrix time series via a tensor CP-decomposition (2021, methodology): “Under certain conditions, VAR processes, multivariate ARCH processes, and multivariate GARCH processes are all α-mixing with exponentially decaying α-mixing coefficients; see Hafner and Preminger (2009), Boussama et al. (2011) and Wong et al. (2020). If we only require maxi∈[p] maxj∈[q] maxt∈[n] P(|”