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Parameter estimation in nonlinear AR-GARCH models

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  • Mika Meitz
  • Pentti Saikkonen

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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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 396.

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Date of creation: 01 Jun 2008
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Handle: RePEc:oxf:wpaper:396

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Keywords: AR-GARCH; Asymptotic normality; Consistency; Nonlinear time series; Quasi maximum likelihood estimation;

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References

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  2. Kristensen Dennis & Rahbek Anders, 2009. "Asymptotics of the QMLE for Non-Linear ARCH Models," Journal of Time Series Econometrics, De Gruyter, De Gruyter, vol. 1(1), pages 1-38, April.
  3. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  4. Mika Meitz & Pentti Saikkonen, 2008. "Parameter estimation in nonlinear AR-GARCH models," Economics Series Working Papers 396, University of Oxford, Department of Economics.
  5. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, Econometric Society, vol. 41(6), pages 997-1016, November.
  6. 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.
  7. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper, Institute of Social and Economic Research, Osaka University 0549, Institute of Social and Economic Research, Osaka University.
  8. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, Elsevier, vol. 1(1), pages 83-106, June.
  9. MEITZ, Mika & SAIKKONEN, Pentti, 2006. "Stability of nonlinear AR-GARCH models," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2006078, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  20. White, Halbert, 1980. "Nonlinear Regression on Cross-Section Data," Econometrica, Econometric Society, Econometric Society, vol. 48(3), pages 721-46, April.
  21. González-Rivera Gloria, 1998. "Smooth-Transition GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 3(2), pages 1-20, July.
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Citations

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Cited by:
  1. Dong Li & Shiqing Ling & Jean-Michel Zakoian, 2013. "Asymptotic Inference in Multiple-Threshold Nonlinear Time Series Models," Working Papers, Centre de Recherche en Economie et Statistique 2013-51, Centre de Recherche en Economie et Statistique.
  2. Lambert, Philippe & Laurent, Sébastien & Veredas, David, 2012. "Testing conditional asymmetry: A residual-based approach," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 36(8), pages 1229-1247.
  3. Mika Meitz & Pentti Saikkonen, 2008. "Parameter estimation in nonlinear AR-GARCH models," Economics Series Working Papers 396, University of Oxford, Department of Economics.
  4. Mika Meitz & Pentti Saikkonen, 2012. "Maximum Likelihood Estimation of a Noninvertible ARMA Model with Autoregressive Conditional Heteroskedasticity," Koç University-TUSIAD Economic Research Forum Working Papers, Koc University-TUSIAD Economic Research Forum 1226, Koc University-TUSIAD Economic Research Forum.
  5. Christophe Chorro & Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2014. "Testing for Leverage Effect in Financial Returns," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00973922, HAL.
  6. KIlIç, Rehim, 2011. "Long memory and nonlinearity in conditional variances: A smooth transition FIGARCH model," Journal of Empirical Finance, Elsevier, Elsevier, vol. 18(2), pages 368-378, March.
  7. Annastiina Silvennoinen & Timo Teräsvirta, 2012. "Modelling conditional correlations of asset returns: A smooth transition approach," CREATES Research Papers 2012-09, School of Economics and Management, University of Aarhus.
  8. Cristina Amado & Timo Teräsvirta, 2011. "Modelling Volatility by Variance Decomposition," CREATES Research Papers 2011-01, School of Economics and Management, University of Aarhus.

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