Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models
AbstractThis paper studies a class of Markov models which consist of two components. Typically, one of the components is observable and the other is unobservable or 'hidden'. Conditions under which (a form of) geometric ergodicity of the unobservable component is inherited by the joint process formed of the two components are given. This immediately implies the existence of initial values such that the joint process is strictly stationary and beta-mixing. In addition to this, conditions for beta-mixing and existence of moments for the joint process are also provided in the case of (possibly) nonstationary initial values. All these results are applied to a general model which includes as special cases various first order generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive conditional duration (ACD) models with possibly complicated nonlinear structures. The results only require mild moment assumptions and in some cases provide necessary and sufficient conditions for geometric ergodicity.
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Bibliographic InfoPaper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 573.
Length: 37 pages
Date of creation: 07 Oct 2004
Date of revision: 20 Apr 2007
Publication status: Published in Econometric Theory, 2008, pages 1291-1320.
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Other versions of this item:
- Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1291-1320, October.
- Mika Meitz & Pentti Saikkonen, 2007. "Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models," Economics Series Working Papers 327, University of Oxford, Department of Economics.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-12-20 (All new papers)
- NEP-ECM-2004-12-20 (Econometrics)
- NEP-ETS-2004-12-20 (Econometric Time Series)
- NEP-FIN-2004-12-20 (Finance)
- NEP-FIN-2004-12-22 (Finance)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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