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Maximum likelihood estimation of STAR and STAR-GARCH models: theory and Monte Carlo evidence

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Author Info

  • Felix Chan

    (Department of Economics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia)

  • Michael McAleer

    (Department of Economics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia)

Abstract

Theoretical and practical interest in non-linear time series models, particularly regime switching models, have increased substantially in recent years. Given the abundant research activity in analysing time-varying volatility through Generalized Autoregressive Conditional Heteroscedasticity (GARCH) processes (see Engle, 1982; Bollerslev, 1986), it is important to analyse regime switching models with GARCH errors. A popular specification in this class is the (stationary) Smooth Transition Autoregressive-GARCH (STAR-GARCH) model. Little is presently known about the structure of the model, or the consistency, asymptotic normality and finite sample properties of the estimators. The paper develops the structural and statistical properties of the STAR-GARCH model, and investigates the finite sample properties of maximum likelihood estimation (MLE) of STAR and STAR-GARCH models through numerical simulation. The effects of fixing the threshold value and|or the transition rate for the STAR model, misspecification of the conditional mean and the transition function of the STAR-GARCH model, and the finite sample properties of the MLE for the STAR-GARCH model, are also examined. These numerical results are used as a guide in empirical research, with an application to Standard and Poor's Composite 500 Index returns for alternative STAR-GARCH models. Copyright © 2002 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/jae.686
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Bibliographic Info

Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 17 (2002)
Issue (Month): 5 ()
Pages: 509-534

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Handle: RePEc:jae:japmet:v:17:y:2002:i:5:p:509-534

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References

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  1. Brooks, Chris & Burke, Simon P. & Persand, Gita, 2001. "Benchmarks and the accuracy of GARCH model estimation," International Journal of Forecasting, Elsevier, vol. 17(1), pages 45-56.
  2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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  4. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April.
  5. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(03), pages 722-729, June.
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  13. Shiqing Ling & Michael McAleer, 2001. "On Adaptive Estimation in Nonstationary ARMA Models with GARCH Errors," ISER Discussion Paper 0548, Institute of Social and Economic Research, Osaka University.
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  15. E.K. Berndt & B.H. Hall & R.E. Hall, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 103-116 National Bureau of Economic Research, Inc.
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Citations

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Cited by:
  1. Chen, Cathy W.S. & Gerlach, Richard H. & Tai, Amanda P.J., 2008. "Testing for nonlinearity in mean and volatility for heteroskedastic models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 489-499.
  2. Beatriz Catalan & F. Javier Trivez, 2007. "Forecasting volatility in GARCH models with additive outliers," Quantitative Finance, Taylor & Francis Journals, vol. 7(6), pages 591-596.
  3. Lai, YiHao & Chen, Cathy W.S. & Gerlach, Richard, 2009. "Optimal dynamic hedging via copula-threshold-GARCH models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2609-2624.
  4. Omay, Tolga, 2012. "The comparison of optimization algorithms on unit root testing with smooth transition," MPRA Paper 42129, University Library of Munich, Germany.
  5. G. Dufrenot & L. Mathieu & V. Mignon, & A. Peguin-Feissolle, 2002. "Persistent misalignments of the European exchange rates : some evidence from nonlinear cointegration," THEMA Working Papers 2002-29, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  6. Pavlidis Efthymios G & Paya Ivan & Peel David A, 2010. "Specifying Smooth Transition Regression Models in the Presence of Conditional Heteroskedasticity of Unknown Form," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(3), pages 1-40, May.
  7. Deschamps, Philippe J., 2007. "Comparing smooth transition and Markov switching autoregressive models of US Unemployment," DQE Working Papers 7, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 04 Jun 2008.
  8. Andreea Halunga & Chris D. Orme, 2007. "First order asymptotic theory for parametric misspecification tests of GARCH models," The School of Economics Discussion Paper Series 0721, Economics, The University of Manchester.
  9. Hwang, Tsorng-Chyi & Chen, Meng-Gu & Chang, Chia-Lin, 2010. "Price Stabilization in the Taiwan Hog and Broiler Industries: Evidence from a STAR Approach," MPRA Paper 15552, University Library of Munich, Germany.
  10. Felix Chan & Michael McAleer & Marcelo C. Medeiros, 2010. "Structure and Asymptotic Theory for Nonlinear Models with GARCH Errors," KIER Working Papers 754, Kyoto University, Institute of Economic Research.
  11. Schleer, Frauke, 2013. "Finding starting-values for maximum likelihood estimation of vector STAR models," ZEW Discussion Papers 13-076, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  12. Tolga Omay, 2011. "The relationship between inflation, output growth, and their uncertainties: Nonlinear Multivariate GARCH-M evidence," Economics Bulletin, AccessEcon, vol. 31(4), pages 3006-3015.
  13. Bildirici, Melike & Ersin, Özgür, 2012. "Nonlinear volatility models in economics: smooth transition and neural network augmented GARCH, APGARCH, FIGARCH and FIAPGARCH models," MPRA Paper 40330, University Library of Munich, Germany, revised May 2012.

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