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Smooth Transition Garch Models: a Bayesian Perspective

Published online by Cambridge University Press:  17 August 2016

Michel Lubrano
Michel Lubrano*
Affiliation:
GREQAM-CNRS, CORE
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Summary

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 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.

Résumé

Résumé

Ce papier propose un nouveau type de modèle GARCH asymétrique où la variance conditionnelle suit deux régimes avec changement graduel. Dans une des deux formulations, la variance conditionnelle réagit différemment aux chocs négatifs et aux chocs positifs, tandis que dans l’autre les gros chocs et les petits chocs ont des effets séparés. L’introduction d’un paramètre de seuil permet de combiner les deux effets. Une stratégie Bayésienne de recherche de spécification pour détecter la présence et la forme de la non-linéarité est construite sur la base d’une comparaison entre les résidus Bayésiens prédictifs et les résidus a posteriori. La méthode est appliquée aux index boursiers de Bruxelles et de Tokyo. Une paramétrisation alternative du modèle GARCH s’avère fort utile pour résoudre certains problèmes numériques.

Keywords

C11C22C51G14C11C22C51G14
Type
Research Article
Information
Recherches Économiques de Louvain/ Louvain Economic Review , Volume 67 , Issue 3 , 2001 , pp. 257 - 287
Copyright
Copyright © Université catholique de Louvain, Institut de recherches économiques et sociales 2001 

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Footnotes

*

GREQAM-CNRS, 2 rue de la Charité, 13002 Marseille, France and CORE, 34 voie du Roman Pays, B-1348 Louvain la Neuve, Belgique, email: lubrano@ehess.cnrs-mrs.fr

References

Bauwens, L. and Lubrano, M., (1991), Bayesian Diagnostics for Heterogeneity, Annales d’Economie et Statistique, 20/21, pp. 17–40.Google Scholar
Bauwens, L. and Lubrano, M., (1998), Bayesian Inference in GARCH Models using the Gibbs Sampler, The Econometrics Journal, 1, pp. C23-C46.Google Scholar
Bauwens, L., Lubrano, M. and Richard, J.F., (1999), Bayesian Inference in Dynamic Econometric Models, Oxford, Oxford University Press.Google Scholar
Bollerslev, T., (1986), Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 31(3), pp. 307–327.Google Scholar
Bollerslev, T., Chou, R.Y. and Kroner, K.F., (1992), ARCH modeling in finance, Journal of Econometrics, 52 (1–2), pp. 5–59.Google Scholar
Carlin, B.P. and Gelfand, A.E., (1991), An iterative Monte Carlo method for non-conjugate Bayesian analysis, Statistics and Computing, 1, pp. 119–128.Google Scholar
Engle, R.F., (1982), Auto-regressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, 50(4), pp. 987–1007.Google Scholar
Engle, R.F. and Bollerslev, T., (1986), Modelling the Persistence of Conditional Variances, Econometric Reviews, 5(1), pp. 1–50.Google Scholar
Engle, R.F. and Mustafa, C., (1992), Implied ARCH Models for Option Prices, Journal of Econometrics, 52 (1–2), pp. 289–311.Google Scholar
Engle, R.F. and Ng, V.K., (1993), Measuring and Testing the Impact of News on Volatility. Journal of Finance, 48(5), pp. 1749–1778.Google Scholar
Engle, R.F., Kane, A. and Noh, J., (1996), Index Option Pricing with Stochastic Volatility and the Value of Accurate Variance Forecasts, Review of Derivatives Research, 1(2), pp. 139–157.Google Scholar
Geweke, J., (1993), Bayesian treatment of the independent Student-i linear model, Journal of Applied Econometrics, 8(0) (Supplement), pp. 19–40.Google Scholar
Geweke, J., (1994), Bayesian Comparison of Econometric Models, Working Paper 532, Research Department, Federal Reserve Bank of Minneapolis.Google Scholar
Glosten, L.R., Jagannathan, R. and Runkle, D.E., (1993), On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks, Journal of Finance 48(5), pp. 1779–1801.Google Scholar
Gonzales-Riviera, G., (1996), Smooth Transition GARCH Models, Working Paper at Department of Economics, University of California at Riverside.Google Scholar
Granger, C.W.J, and Terasvirta, T., (1993), Modelling non-linear economic relationships, Oxford, Oxford University Press.Google Scholar
Hagerud, G.E. (1997) A New Non-linear GARCH Model, PhD Dissertation, Stockholm School of Economics.Google Scholar
Jansen, E.S. and Terasvirta, T., (1996), Testing Parameter Constancy and Super Exogeneity in Econometric Equations, Oxford Bulletin of Economics and Statistics, 58(4), pp. 735–763.Google Scholar
Kleibergen, F. and van Dijk, H.K., (1993), Non-stationarity in GARCH Models: A Bayesian Analysis, Journal of Applied Econometrics, 8(0), Supplement, pp. S41-S61.Google Scholar
Lubrano, M., (2000), Bayesian Analysis of Non-linear Time Series with Models with a Threshold, in Barnett, W.A., Hendry, D.F., Hylleberg, S. Teräsvirta, T. Tjostheim, D. and Wiirtz, A. (eds), Non-linear Econometric Modelling, Cambridge University Press, pp. 79–118.Google Scholar
Luukkonen, R., Saikkonen, P. and Terasvirta, T., (1988), Testing Linearity against Smooth Transition Autoregression, Biometrika, 75, pp. 491–499.Google Scholar
Nelson, D.B., (1990), Stationarity and persistence in the GARCH(1,1) model, Econometric Theory, 6(3), pp. 318–334.Google Scholar
Nelson, D.B., (1991), Conditional heteroskedasticity in asset returns: A new approach, Econometrica, 59(2), pp. 347–370.Google Scholar
Noh, J., Engle, R.F. and Kane, A., (1995), Forecasting Volatility and Option Prices of the SP500 Index, In Engle Robert, F., ed. ARCH: Selected readings, Advanced Texts in Econometrics, Oxford and New York: Oxford University Press, pp. 314–331.Google Scholar
Osiewalski, J. and Welfe, A., (1998), The Wage-Price Mechanism: An Endogenous Switching Model, European Economic Review, 42(2), pp. 365–374.Google Scholar
Pagan, A., (1996), The econometrics of financial markets, Journal of Empirical Finance, 3, pp. 15–102.Google Scholar
Pagan, A. and Schwert, G.W., (1990), Alternative Models for Conditional Stock Volatility, Journal of Econometrics, 45 (1–2), pp. 267–290.Google Scholar
Robert, C.P. and Mengersen, K.L., (1995), Reparameterisation Issues in Mixture Modelling and their Bearing on the Gibbs Sampler, CREST-INSEE Discussion Paper No 9538.Google Scholar
Susmel, R. and Engle, R.F., (1994), Hourly Volatility Spillovers between International Equity Markets, Journal of International Money and Finance, 13(1), pp. 3–25.Google Scholar
Terasvirta, T., (1994) Specification, Estimation and Evaluation of Smooth Transition Autoregressive Models, Journal of the American Statistical Association, 89(425), pp. 208–218.Google Scholar
Zakoian, J.M., (1994), Threshold Heteroskedastic Models, Journal of Economic Dynamics and Control, 18(5), pp. 931–955.Google Scholar
Zellner, A., (1975), Bayesian Analysis of Regression Error Terms, Journal of the American Statistical Association, 70, pp. 138–144.Google Scholar