Parameter Estimation in Nonlinear AR-GARCH Models

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Parameter Estimation in Nonlinear AR-GARCH Models

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Mika Meitz
Pentti Saikkonen

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Mika Meitz

Abstract

This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a functional coefficient autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. Strong consistency and asymptotic normality of the global Gaussian quasi maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors.

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Paper provided by European University Institute in its series Economics Working Papers with number ECO2008/25.

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Date of creation: 2008
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Handle: RePEc:eui:euiwps:eco2008/25

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Paper
- 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 Series Working Papers 396, University of Oxford, Department of Economics. [Downloadable!]

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

This paper has been announced in the following NEP Reports:

NEP-ALL-2008-06-13 (All new papers)
NEP-ECM-2008-06-13 (Econometrics)
NEP-ETS-2008-06-13 (Econometric Time Series)
NEP-ORE-2008-06-13 (Operations Research)

References listed on IDEAS
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Kristensen, Dennis & Rahbek, Anders, 2005. "ASYMPTOTICS OF THE QMLE FOR A CLASS OF ARCH(q) MODELS," Econometric Theory, Cambridge University Press, vol. 21(05), pages 946-961, October. [Downloadable!]
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. [Downloadable!]
Other versions:
- 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!]
- 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. [Downloadable!]
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Other versions:
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Other versions:
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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!]
- MEITZ, Mika & SAIKKONEN, Pentti, 2006. "Stability of nonlinear AR-GARCH models," CORE Discussion Papers 2006078, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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Other versions:
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