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Smooth-Transition GARCH Models

Author

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  • González-Rivera Gloria

    (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.

Suggested Citation

  • González-Rivera Gloria, 1998. "Smooth-Transition GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(2), pages 1-20, July.
    • Handle: RePEc:bpj:sndecm:v:3:y:1998:i:2:n:1
    DOI: 10.2202/1558-3708.1041
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