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Hierarchical hidden Markov structure for dynamic correlations: the hierarchical RSDC model (version révisée)

  • Philippe Charlot

    ()

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579)

  • Vêlayoudom Marimoutou

    ()

    (IFP - Institut Français de Pondichéry - Ministère des Affaires étrangères et européennes - CNRS : UMIFRE21)

This paper presents a new multivariate GARCH model with time-varying conditional correlation structure, which is a special case of the Regime Switching Dynamic Correlation (RSDC) of Pelletier (2006). This model which we have named Hierarchical RSDC (HRSDC), has been built with the hierarchical generalization of the hidden Markov model introduced by Fine et al. (1998). This can be viewed graphically as a tree-structure with different types of states. The former are called production states, and they can emit observations, as in the class of Markov-Switching approach. The latter are called "abstract" states. They can't emit observations but establish vertical and horizontal probabilities that define the dynamic of the hidden hierarchical structure. The main advantage of this approach, comparable to the classical Markov-Switching model, is that it improves the granularity of the regimes. Our model is also comparable to the new Double Smooth Transition Conditional Correlation GARCH model (DSTCC), a STAR approach for dynamic correlations proposed by Silvennoinen and Terasvirta (2007). The reason is that, under certain assumptions, the DSTCC and our model represent two classical competing approaches to modeling regime switching. We performed, Monte-Carlo simulations, and we applied the model to two empirical applications in studying the conditional correlations of selected stock returns. Results show that the HRSDC provides a good measure of the correlations, and possesses an interesting explanatory power.

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Paper provided by HAL in its series Working Papers with number hal-00605965.

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Date of creation: 2011
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Handle: RePEc:hal:wpaper:hal-00605965
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  1. Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Modelling Multivariate Autoregressive Conditional Heteroskedasticity with the Double Smooth Transition Conditional Correlation GARCH Model," CREATES Research Papers 2008-05, School of Economics and Management, University of Aarhus.
  2. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
  3. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  4. Kim, C-J., 1991. "Dynamic Linear Models with Markov-Switching," Papers 91-8, York (Canada) - Department of Economics.
  5. Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
  6. Denis Pelletier, 2004. "Regime Switching for Dynamic Correlations," Econometric Society 2004 North American Summer Meetings 230, Econometric Society.
  7. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
  8. Annastiina Silvennoinen & Timo Teräsvirta, 2005. "Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations," Research Paper Series 168, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Multivariate GARCH models," CREATES Research Papers 2008-06, School of Economics and Management, University of Aarhus.
  10. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
  11. Engle, Robert & Colacito, Riccardo, 2006. "Testing and Valuing Dynamic Correlations for Asset Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 238-253, April.
  12. Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July.
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