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Smooth Transition Garch Models : a Baysian Perspective

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  • Michel LUBRANO

    (GREQAM-CNRS)

Abstract

This paper proposes a new kind of asymmetric GARCH where the conditional variance obeys two différent 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 mixed effect. A Bayesian strategy, based on the comparison between posterior and predictive Bayesian residuals, is built for detecting the presence and the shape of non-linearities. The method is applied to the Brussels and Tokyo stock indexes. The attractiveness of an alternative parameterisation of the GARCH model is emphasised as a potential solution to some numerical problems.

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Paper provided by Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) in its series Discussion Papers (REL - Recherches Economiques de Louvain) with number 2001032.

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Length: 32
Date of creation: 01 Sep 2001
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Handle: RePEc:ctl:louvre:2001032

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  1. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
  2. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
  3. Lubrano, M., 1998. "Bayesian Analysis of Nonlinear Time Series Models with a Threshold," G.R.E.Q.A.M. 98a13, Universite Aix-Marseille III.
  4. 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.
  5. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139, September.
  6. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  7. Susmel, Raul & Engle, Robert F., 1994. "Hourly volatility spillovers between international equity markets," Journal of International Money and Finance, Elsevier, vol. 13(1), pages 3-25, February.
  8. BAUWENs, Luc & LUBRANO , Michel, 1996. "Bayesian Inference on GARCH Models using the Gibbs Sampler," CORE Discussion Papers 1996027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Jansen, Eilev S. & Teräsvirta, Timo, 1995. "Testing Parameter Constancy and super Exogeneity in Econometric Equations," Working Paper Series in Economics and Finance 53, Stockholm School of Economics.
  10. Nicole FORTIN, 1991. "Fonctions de production et biais d'agrégation," Annales d'Economie et de Statistique, ENSAE, issue 20-21, pages 41-68.
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  12. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 289-311.
  13. Kleibergen, F & Van Dijk, H K, 1993. "Non-stationarity in GARCH Models: A Bayesian Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S41-61, Suppl. De.
  14. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  15. Osiewalski, Jacek & Welfe, Aleksander, 1998. "The price-wage mechanism: An endogenous switching model," European Economic Review, Elsevier, vol. 42(2), pages 365-374, February.
  16. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
  17. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  18. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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Cited by:
  1. 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.
  2. Bauwens, Luc & Lubrano, Michel, 2002. "Bayesian option pricing using asymmetric GARCH models," Journal of Empirical Finance, Elsevier, vol. 9(3), pages 321-342, August.
  3. BAUWENS, Luc & STORTI, Giuseppe, 2007. "A component GARCH model with time varying weights," CORE Discussion Papers 2007019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. LUBRANO, Michel, 2000. "Bayesian non-linear modellings of the short term US interest rate: the help of non-parametric tools," CORE Discussion Papers 2000038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Michael Dueker & Zacharias Psaradakis & Martin Sola & Fabio Spagnolo, 2009. "Contemporaneous-Threshold Smooth Transition GARCH Models," Department of Economics Working Papers 2009-06, Universidad Torcuato Di Tella.

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