Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models

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Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models

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Mika Meitz
Pentti Saikkonen

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Mika Meitz

Abstract

This 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 geometric ergodicity of the unobservable component is inherited by the joint process formed of the two components are given. This implies existence of initial values such that the joint process is strictly stationary and ?-mixing. In addition to this, conditions for the existence of moments are also obtained and extensions to the case of nonstationary initial values are provided. 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 non-linear structures. The results only require mild moment assumptions and in some cases provide necessary and sufficient conditions for geometric ergodicity.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 327.

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Date of creation: 2007
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Handle: RePEc:oxf:wpaper:327

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Paper
- Meitz, Mika & Saikkonen, Pentti, 2004. "Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models," Working Paper Series in Economics and Finance 573, Stockholm School of Economics, revised 20 Apr 2007. [Downloadable!]

Find related papers by JEL classification:
C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models

This paper has been announced in the following NEP Reports:

NEP-ALL-2007-05-19 (All new papers)
NEP-ECM-2007-05-19 (Econometrics)
NEP-ETS-2007-05-19 (Econometric Time Series)
NEP-ICT-2007-05-19 (Information & Communication Technologies)

References listed on IDEAS
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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Other versions:
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Full references

Cited by:
(explanations, 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.)

Meitz, Mika & Saikkonen, Pentti, 2006. "Stability of nonlinear AR-GARCH models," Working Paper Series in Economics and Finance 632, Stockholm School of Economics. [Downloadable!]
Other versions:
- Mika Meitz & Pentti Saikkonen, 2007. "Stability of nonlinear AR-GARCH models," Economics Series Working Papers 328, University of Oxford, Department of Economics. [Downloadable!]
- Mika Meitz & Pentti Saikkonen, 2008. "Stability of nonlinear AR-GARCH models," Journal of Time Series Analysis, Blackwell Publishing, vol. 29(3), pages 453-475, 05. [Downloadable!] (restricted)
Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Modelling Multivariate Autoregressive Conditional Heteroskedasticity with the Double Smooth Transition Conditional Correlation GARCH model," Working Paper Series in Economics and Finance 0652, Stockholm School of Economics. [Downloadable!]
Other versions:
- Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Modelling Multivariate Autoregressive Conditional Heteroskedasticity with the Double Smooth Transition Conditional Correlation GARCH Model," CREATES Research Papers 2008-05, School of Economics and Management, University of Aarhus. [Downloadable!]
Mika Meitz & Pentti Saikkonen, 2008. "Parameter estimation in nonlinear AR-GARCH models," Economics Series Working Papers 396, University of Oxford, Department of Economics. [Downloadable!]
Other versions:
- Mika Meitz & Pentti Saikkonen, 2008. "Parameter estimation in nonlinear AR-GARCH models," CREATES Research Papers 2008-30, School of Economics and Management, University of Aarhus. [Downloadable!]
- Mika Meitz & Pentti Saikkonen, 2008. "Parameter Estimation in Nonlinear AR-GARCH Models," Economics Working Papers ECO2008/25, European University Institute. [Downloadable!]

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