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

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

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)

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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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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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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.:

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. [Downloadable!]
Other versions:
- Shiqing Ling & Michael McAleer, 2001. "Necessary and Sufficient Moment Conditions for the GARCH(r,s) and Asymmetric Power GARCH(r,s) Models," ISER Discussion Paper 0534, Institute of Social and Economic Research, Osaka University. [Downloadable!]
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Other versions:
- Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University. [Downloadable!]
Franses, Ph.H.B.F. & Neele, J. & Dijk, D.J.C. van, 1998. "Forecasting volatility with switching persistence GARCH models," Econometric Institute Report EI 9819 Revision_Date: 20, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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Other versions:
- Shiqing Ling & Michael McAleer, 2001. "Stationarity and the Existence of Moments of a Family of GARCH Processes," ISER Discussion Paper 0535, Institute of Social and Economic Research, Osaka University. [Downloadable!]
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, vol. 1(1), pages 83-106, June. [Downloadable!] (restricted)
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- He, Changli & Teräsvirta, Timo, 1997. "Properties of Moments of a Family of GARCH Processes," Working Paper Series in Economics and Finance 198, Stockholm School of Economics.

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.)

David Peel & Ivan Paya & E Pavlidis, 2009. "Specifying Smooth Transition Regression Models in the Presence of Conditional Heteroskedasticity of Unknown Form," Working Papers 005913, Lancaster University Management School, Economics Department. [Downloadable!]
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. [Downloadable!]
Other versions:
- Gilles DUFRENOT & Laurent MATHIEU & Val=E9rie MIGNON & Anne PEGUIN-FEISSOLE, 2003. "Persistent misalignments of the European exchanges rates: some evidence from nonlinear cointegration," International Finance 0309003, EconWPA. [Downloadable!]
- Gilles Dufrénot & Laurent Mathieu & Valérie Mignon & Anne Péguin-Feissolle, 2006. "Persistent misalignments of the European exchange rates: some evidence from non-linear cointegration," Applied Economics, Taylor and Francis Journals, vol. 38(2), pages 203-229, February. [Downloadable!] (restricted)
Philippe J. Deschamps, 2008. "Comparing smooth transition and Markov switching autoregressive models of US unemployment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 435-462. [Downloadable!]
Other versions:
- Philippe J. Deschamps, 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. [Downloadable!]
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. [Downloadable!]
Other versions:
- Halunga, Andreea G. & Orme, Chris D., 2009. "First-Order Asymptotic Theory For Parametric Misspecification Tests Of Garch Models," Econometric Theory, Cambridge University Press, vol. 25(02), pages 364-410, April. [Downloadable!]

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