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Smooth-Transition GARCH Models

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Author Info
Gloria González-Rivera (University of California, Riverside)
Abstract

The asymmetric response of conditional variances to positive versus negative news has been traditionally modeled with threshold specifications that allow only two possible regimes: low or high volatility. In this paper, the possibility of intermediate regimes is considered and modeled with the introduction of a smooth-transition mechanism in a GARCH specification. One important property of this model is that it permits an on-off ARCH effect, in which a time series can switch from a process with constant variance to a process with time-varying variance. On testing for the existence of a smooth-transition mechanism, there are nuisance parameters that are not identified under the null hypothesis. Nevertheless, it is possible to construct a Lagrange-multiplier test that is ¬2 p -distributed. A Monte Carlo simulation shows that the test has very good size and good power. A smooth-transition GARCH specification is tested and estimated with stock returns and exchange-rate data. While a threshold model is preferred for stock returns, a smooth-transition model is more likely for exchange rates.

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Publisher Info
Article provided by Berkeley Electronic Press in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 3 (1998)
Issue (Month): 2 ()
Pages: 61-78
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Handle: RePEc:bep:sndecm:3:1998:2:61-78

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Related research
Keywords: GARCH leverage effect news-impact curve smooth transition threshold

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.:

  1. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November. [Downloadable!] (restricted)
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  2. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-78, December. [Downloadable!] (restricted)
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  3. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March. [Downloadable!] (restricted)
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  4. Dueker, Michael J, 1997. "Markov Switching in GARCH Processes and Mean-Reverting Stock-Market Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 26-34, January.
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  5. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September. [Downloadable!] (restricted)
  6. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  7. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December. [Downloadable!] (restricted)
  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, vol. 1(1), pages 83-106, June. [Downloadable!] (restricted)
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  9. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333. [Downloadable!] (restricted)
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  10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
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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.)

  1. Mika Meitz & Pentti Saikkonen, 2008. "Parameter Estimation in Nonlinear AR-GARCH Models," Economics Working Papers ECO2008/25, European University Institute. [Downloadable!]
    Other versions:
  2. 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!]
  3. Jonathan B. Hill, 2004. "LM-Tests for Linearity Against Smooth Transition Alternatives: A Bootstrap Simulation Study," Working Papers 0412, Florida International University, Department of Economics. [Downloadable!]
    Other versions:
  4. L. Grossi & G. Morelli, 2006. "Robust volatility forecasts and model selection in financial time series," Economics Department Working Papers 2006-SE02, Department of Economics, Parma University (Italy). [Downloadable!]
  5. Changli He & Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Parameterizing unconditional skewness in models for financial time series," CREATES Research Papers 2008-07, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  6. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," Working Paper Series in Economics and Finance 646, Stockholm School of Economics. [Downloadable!]
  7. Meitz, Mika & Teräsvirta, Timo, 2004. "Evaluating models of autoregressive conditional duration," Working Paper Series in Economics and Finance 557, Stockholm School of Economics, revised 13 Dec 2004. [Downloadable!]
    Other versions:
  8. Jonathan B. Hill, 2004. "Consistent and Non-Degenerate Model Specification Tests Against Smooth Transition Alternatives," Working Papers 0406, Florida International University, Department of Economics. [Downloadable!]
  9. Malmsten, Hans, 2004. "Evaluating exponential GARCH models," Working Paper Series in Economics and Finance 564, Stockholm School of Economics, revised 03 Sep 2004. [Downloadable!]
  10. M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2001. "Outliers And Conditional Autoregressive Heteroscedasticity In Time Series," Statistics and Econometrics Working Papers ws010704, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
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