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Stability of nonlinear AR-GARCH models Author info | Abstract | Publisher info | Download info | Related research | Statistics Mika Meitz
Pentti Saikkonen
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This article studies the stability of nonlinear autoregressive models with conditionally 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 &bgr;-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. Copyright 2008 The Authors
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Article provided by Blackwell Publishing in its journal Journal of Time Series Analysis .
Volume (Year): 29 (2008)
Issue (Month): 3 (05)
Pages: 453-475
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Handle: RePEc:bla:jtsera:v:29:y:2008:i:3:p:453-475Contact details of provider: Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782
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Paper 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!] Meitz, Mika & Saikkonen, Pentti, 2006.
"Stability of nonlinear AR-GARCH models ,"
Working Paper Series in Economics and Finance
632, Stockholm School of Economics.
[Downloadable!] 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.: 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!] 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!] 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) 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)
Other versions:
van Dijk, Dick & Teräsvirta, Timo & Franses, Philip Hans, 2000.
"Smooth Transition Autoregressive Models - A Survey of Recent Developments ,"
Working Paper Series in Economics and Finance
380, Stockholm School of Economics, revised 17 Jan 2001.
[Downloadable!] D. van Dijk & T. Terasvirta & P.H. Franses, 2000.
"Smooth transition autoregressive models - A survey of recent developments ,"
Econometric Institute Report
200, Erasmus University Rotterdam, Econometric Institute.
[Downloadable!] Dijk, D.J.C. van & Terasvirta, T. & Franses, Ph.H.B.F., 2000.
"Smooth transition autoregressive models - A survey of recent developments ,"
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Ling, Shiqing & McAleer, Michael, 2003.
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Econometric Theory ,
Cambridge University Press, vol. 19(02), pages 280-310, April.
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"A note on the ergodicity of non-linear autoregressive model ,"
Statistics & Probability Letters ,
Elsevier, vol. 34(4), pages 365-372, June.
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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.
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Other versions: 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.
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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, February.
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Lundbergh, Stefan & Terasvirta, Timo, 2002.
"Evaluating GARCH models ,"
Journal of Econometrics ,
Elsevier, vol. 110(2), pages 417-435, October.
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Other versions: Lu, Zudi & Jiang, Zhenyu, 2001.
"L1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term ,"
Statistics & Probability Letters ,
Elsevier, vol. 51(2), pages 121-130, January.
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Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity ,"
Journal of Econometrics ,
Elsevier, vol. 31(3), pages 307-327, April.
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Lee, Chanho, 1998.
"Asymptotics of a class of pth-order nonlinear autoregressive processes ,"
Statistics & Probability Letters ,
Elsevier, vol. 40(2), pages 171-177, September.
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Cline, Daren B. H. & Pu, Huay-min H., 1998.
"Verifying irreducibility and continuity of a nonlinear time series ,"
Statistics & Probability Letters ,
Elsevier, vol. 40(2), pages 139-148, September.
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M. Lanne & P. Saikkonen, .
"Nonlinear GARCH Models for Highly Persistent Volatility ,"
Sonderforschungsbereich 373
2002-20, Humboldt Universitaet Berlin.
Other versions: 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!]
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!] 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!]
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.)
Mika Meitz & Pentti Saikkonen, 2008.
"Parameter Estimation in Nonlinear AR-GARCH Models ,"
Economics Working Papers
ECO2008/25, European University Institute.
[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!]
Other versions:
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!] Meitz, Mika & Saikkonen, Pentti, 2006.
"Stability of nonlinear AR-GARCH models ,"
Working Paper Series in Economics and Finance
632, Stockholm School 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)
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