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Smooth Transition Garch Models : a Baysian Perspective

  • Michel LUBRANO

    (GREQAM-CNRS)

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
Date of revision:
Handle: RePEc:ctl:louvre:2001032
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  1. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
  2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  3. 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.
  4. Jansen, Eilev S. & Teräsvirta, Timo, 1995. "Testing Parameter Constancy and super Exogeneity in Econometric Equations," SSE/EFI Working Paper Series in Economics and Finance 53, Stockholm School of Economics.
  5. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  6. Osiewalski, Jacek & Welfe, Aleksander, 1998. "The price-wage mechanism: An endogenous switching model," European Economic Review, Elsevier, vol. 42(2), pages 365-374, February.
  7. Nicole FORTIN, 1991. "Fonctions de production et biais d'agrégation," Annales d'Economie et de Statistique, ENSAE, issue 20-21, pages 41-68.
  8. Luc Bauwens & Michel Lubrano, 1998. "Bayesian inference on GARCH models using the Gibbs sampler," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C23-C46.
  9. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 289-311.
  10. John F. Geweke, 1994. "Bayesian comparison of econometric models," Working Papers 532, Federal Reserve Bank of Minneapolis.
  11. 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.
  12. 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.
  13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  14. Lubrano, M., 1996. "Bayesian Analysis of Nonlinear Time Series Models with Threshold," G.R.E.Q.A.M. 96a12, Universite Aix-Marseille III.
  15. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
  16. Pagan, A.R. & Schwert, G.W., 1989. "Alternative Models For Conditional Stock Volatility," Papers 89-02, Rochester, Business - General.
  17. 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.
  18. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
  19. Robert F. Engle & Alex Kane & Jaesun Noh, 1993. "Index-Option Pricing with Stochastic Volatility and the Value of Accurate Variance Forecasts," NBER Working Papers 4519, National Bureau of Economic Research, Inc.
  20. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139.
  21. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
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