Hierarchical Hidden Markov Structure for Dynamic Correlations: The Hierarchical RSDC Model

34 Pages Posted: 14 Oct 2008 Last revised: 16 Oct 2008

See all articles by Charlot Philippe

Charlot Philippe

Universities of Marseille; Groupement de Recherche en Economie Quantitative d'Aix-Marseille

Vêlayoudom Marimoutou

Université de la Mediterraneé

Date Written: October 15, 2008

Abstract

This paper presents a new multivariate GARCH model with time-varying conditional correlation structure which is a generalization of the Regime Switching Dynamic Correlation (RSDC) of Pelletier (2006). This model, which we name Hierarchical RSDC, is building 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 first are called production states and they can emit observations, as in the classical Markov-Switching approach. The second 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 gain of this approach compared to the classical Markov-Switching model is to increase the granularity of the regimes. Our model is also compared 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 also perform Monte-Carlo simulations and we apply the model to two empirical applications studying the conditional correlations of selected stock returns. Results show that the Hierarchical RSDC provides a good measure of the correlations and also has an interesting explanatory power.

Keywords: Multivariate GARCH, Dynamic correlations, Regime switching, Markov chain, Hidden Markov models, Hierarchical Hidden Markov models

Suggested Citation

Philippe, Charlot and Marimoutou, Vêlayoudom, Hierarchical Hidden Markov Structure for Dynamic Correlations: The Hierarchical RSDC Model (October 15, 2008). AFFI/EUROFIDAI, Paris December 2008 Finance International Meeting AFFI - EUROFIDAI . Available at SSRN: https://ssrn.com/abstract=1283178 or http://dx.doi.org/10.2139/ssrn.1283178

Charlot Philippe (Contact Author)

Universities of Marseille ( email )

Groupement de Recherche en Economie Quantitative d'Aix-Marseille ( email )

Centre de la Vieille Charité
2 rue de la Charité
Marseille, 13236
France

Vêlayoudom Marimoutou

Université de la Mediterraneé ( email )

GREQAM
Centre de la Vieille Charite
13002 Marseille
France

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