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Stability of nonlinear AR-GARCH models

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Author Info
Mika Meitz
Pentti Saikkonen

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Abstract

This paper studies the stability of nonlinear autoregressive models with conditionality heteroskedastic errors. We consider a nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a nonlinear first order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. Conditions under which the model is stable in the sense that its Markov chain representation is geometrically ergodic are provided. This implies the existence of an initial distribution such that the process is strictly stationary and ?-mixing. Conditions under which the stationary distribution has finite moments are also given. The results cover several nonlinear specifications recently proposed for both the conditional mean and conditional variance, and only require mild moment conditions.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 328.

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Date of creation: 2007
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Handle: RePEc:oxf:wpaper:328

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Keywords: Nonlinear Autoregression Generalized Autoregressive Conditional Heteroskedasticity Nonlinear Time Series Models Geometric Ergodicity Mixing Strict Stationarity Existence of Moments Markov Models

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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

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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.:
  1. Meitz, Mika & Saikkonen, Pentti, 2006. "Stability of nonlinear AR-GARCH models," Working Paper Series in Economics and Finance 632, Stockholm School of Economics. [Downloadable!]
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  2. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, March. [Downloadable!]
  3. Dick van Dijk & Timo Teräsvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models - A Survey Of Recent Developments," Econometric Reviews, Taylor and Francis Journals, vol. 21(1), pages 1-47. [Downloadable!] (restricted)
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  4. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  5. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc. [Downloadable!] (restricted)
  6. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, January. [Downloadable!]
  7. Lundbergh, Stefan & Terasvirta, Timo, 2002. "Evaluating GARCH models," Journal of Econometrics, Elsevier, vol. 110(2), pages 417-435, October. [Downloadable!] (restricted)
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  8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  9. M. Lanne & P. Saikkonen, . "Nonlinear GARCH Models for Highly Persistent Volatility," Sonderforschungsbereich 373 2002-20, Humboldt Universitaet Berlin.
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  10. 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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(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.)

  1. Mika Meitz & Pentti Saikkonen, 2007. "Stability of nonlinear AR-GARCH models," Economics Series Working Papers 328, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
  2. 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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