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Smooth transition GARCH models: a Bayesian perspective

  • 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)

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.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1998066.

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Date of creation: 01 Dec 1998
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Handle: RePEc:cor:louvco:1998066
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  1. 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.
  2. Lubrano, M., 1996. "Bayesian Analysis of Nonlinear Time Series Models with Threshold," G.R.E.Q.A.M. 96a12, Universite Aix-Marseille III.
  3. 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).
  4. 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.
  5. Pagan, A.R. & Schwert, G.W., 1989. "Alternative Models For Conditional Stock Volatility," Papers 89-02, Rochester, Business - General.
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  7. 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.
  8. 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.
  9. 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.
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  11. Jansen, Eilev S & Terasvirta, Timo, 1996. "Testing Parameter Constancy and Super Exogeneity in Econometric Equations," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 735-63, November.
  12. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139.
  13. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
  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. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  17. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  18. 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.
  19. John F. Geweke, 1994. "Bayesian comparison of econometric models," Working Papers 532, Federal Reserve Bank of Minneapolis.
  20. Nicole FORTIN, 1991. "Fonctions de production et biais d'agrégation," Annales d'Economie et de Statistique, ENSAE, issue 20-21, pages 41-68.
  21. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 289-311.
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