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Factor Analysed Hidden Markov Models for Conditionally Heteroscedastic Financial Time Series

Christian Lavergne 1, 2 Mohamed Saidane 1
2 VIRTUAL PLANTS - Modeling plant morphogenesis at different scales, from genes to phenotype
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique, UMR AGAP - Amélioration génétique et adaptation des plantes méditerranéennes et tropicales
Abstract : In this article we develop a new approach within the framework of asset pricing models that incorporates two key features of the latent volatility: co-movement among conditionally heteroscedastic financial returns and switching between different unobservable regimes. By combining latent factor models with hidden Markov chain models (HMM) we derive a dynamical local model for segmentation and prediction of multivariate conditionally heteroscedastic financial time series. We concentrate, more precisely on situations where the factor variances are modeled by univariate GQARCH processes. The intuition behind our approach is the use a piece-wise multivariate and linear process - which we can also regard as a mixed-state dynamic linear system - for modeling the regime switches. In particular, we supposed that the observed series can be modeled using a time varying parameter model with the assumption that the evolution of these parameters is governed by a first-order hidden Markov process. The EM algorithm that we have developed for the maximum likelihood estimation, is based on a quasi-optimal switching Kalman filter approach combined with a Viterbi approximation which yield inferences about the unobservable path of the common factors, their variances and the latent variable of the state process. Extensive Monte Carlo simulations and preliminary experiments obtained with daily foreign exchange rate returns of eight currencies show promising results.
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https://hal.inria.fr/inria-00070164
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Submitted on : Friday, May 19, 2006 - 7:18:15 PM
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  • HAL Id : inria-00070164, version 1
  • PRODINRA : 250252

Citation

Christian Lavergne, Mohamed Saidane. Factor Analysed Hidden Markov Models for Conditionally Heteroscedastic Financial Time Series. [Research Report] RR-5862, INRIA. 2006, pp.48. ⟨inria-00070164⟩

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