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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 - ECM - Ecole Centrale de Marseille - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales - Université Paul Cézanne - Aix-Marseille 3 - Université de la Méditerranée - Aix-Marseille 2 - CNRS - Centre National de la Recherche Scientifique)

  • Vêlayoudom Marimoutou

    ()

    (IFP - Institut Français de Pondichéry - CNRS - Centre National de la Recherche Scientifique - Ministère des Affaires étrangères et européennes)

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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Date of creation: 2011
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Handle: RePEc:hal:wpaper:hal-00605965
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  1. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
  3. Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Multivariate GARCH models," CREATES Research Papers 2008-06, Department of Economics and Business Economics, Aarhus University.
  4. Silvennoinen, Annastiina & Teräsvirta, Timo, 2005. "Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations," SSE/EFI Working Paper Series in Economics and Finance 577, Stockholm School of Economics, revised 01 Oct 2005.
  5. Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
  6. 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.
  7. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Modelling Multivariate Autoregressive Conditional Heteroskedasticity with the Double Smooth Transition Conditional Correlation GARCH model," SSE/EFI Working Paper Series in Economics and Finance 0652, Stockholm School of Economics.
  8. 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.
  9. 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.
  10. 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.
  11. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
  12. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
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