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Smooth transition GARCH models: a Bayesian perspective

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  • LUBRANO, Michel

    (GREQAM-CNRS, 2 rue de la Charité, 13002 Marseille, France and Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

Abstract

This paper proposes a new kind of asymmetric GARCH where the conditional variance obeys two different regimes with a smooth transition function. In one formulation, the conditional variance reacts differently to negative and positive shocks while in a second formulation, small and big shocks have separate effects. The introduction of a threshold allows for a mixedeffect. A Bayesian strategy, based on the comparison between posterior and predictive Bayesian residuals, is built for detecting the presence and the shape of nonlinearities. The method is applied to the Brussels and Tokyo stock indexes. The need for an alternative parameterisation of the GARCH model is emphasised as a solution to numerical problems.

Suggested Citation

  • LUBRANO, Michel, 1998. "Smooth transition GARCH models: a Bayesian perspective," LIDAM Discussion Papers CORE 1998066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:1998066
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    Cited by:

    1. Bauwens Luc & Storti Giuseppe, 2009. "A Component GARCH Model with Time Varying Weights," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(2), pages 1-33, May.
    2. LUBRANO, Michel, 2000. "Bayesian non-linear modellings of the short term US interest rate: the help of non-parametric tools," LIDAM Discussion Papers CORE 2000038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Fonseca, Thais C O & Cerqueira, Vinicius S & Migon, Helio S & Torres, Christian A C, 2021. "Evaluating the performance of degrees of freedom estimation in asymmetric GARCH models with t-student innovations," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 40(2), April.
    4. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    5. Thomas Chuffart, 2015. "Selection Criteria in Regime Switching Conditional Volatility Models," Econometrics, MDPI, vol. 3(2), pages 1-28, May.
    6. Bauwens, Luc & Lubrano, Michel, 2002. "Bayesian option pricing using asymmetric GARCH models," Journal of Empirical Finance, Elsevier, vol. 9(3), pages 321-342, August.
    7. Wago, Hajime, 2004. "Bayesian estimation of smooth transition GARCH model using Gibbs sampling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(1), pages 63-78.
    8. Dueker Michael J. & Psaradakis Zacharias & Sola Martin & Spagnolo Fabio, 2011. "Contemporaneous-Threshold Smooth Transition GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-25, March.
    9. Martin Bruns & Michele Piffer, 2021. "Monetary policy shocks over the business cycle: Extending the Smooth Transition framework," University of East Anglia School of Economics Working Paper Series 2021-07, School of Economics, University of East Anglia, Norwich, UK..
    10. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    11. Lin, Edward M.H. & Chen, Cathy W.S. & Gerlach, Richard, 2012. "Forecasting volatility with asymmetric smooth transition dynamic range models," International Journal of Forecasting, Elsevier, vol. 28(2), pages 384-399.
    12. Glen Livingston Jr & Darfiana Nur, 2020. "Bayesian estimation and model selection of a multivariate smooth transition autoregressive model," Environmetrics, John Wiley & Sons, Ltd., vol. 31(6), September.

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    More about this item

    Keywords

    Bayesian; asymmetric GARCH; specification tests; nonlinear modelling; stock indexes;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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