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Testing for the number of states in hidden Markov models

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  • Holzmann, Hajo
  • Schwaiger, Florian

Abstract

Scale mixtures of normal distributions are frequently used to model the heavy tails of asset returns. A simple specification is a three component scale mixture, where the states correspond to high, intermediate and low volatility phases of the market. Tests for the number of states in hidden Markov models are proposed and used to assess whether in view of recent financial turbulences, three volatility states are still sufficient. The tests extend tests for independent finite mixtures by using a quasi-likelihood which neglects the dependence structure of the regime. The main theoretical insight is the surprising fact that the asymptotic distribution of the proposed tests for HMMs is the same as for independent mixtures with corresponding weights. As application the number of volatility states for logarithmic returns of the S&P 500 index in two HMMs is determined, one with state-dependent normal distributions and switching mean and scale, and the other with state-dependent skew-normal distributions with switching scale and structural mean and skewness parameters. It turns out that in both models, four states are indeed required, and a maximum-a-posteriori analysis shows that the highest volatility state mainly corresponds to the recent financial crisis.

Suggested Citation

  • Holzmann, Hajo & Schwaiger, Florian, 2016. "Testing for the number of states in hidden Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 318-330.
    • Handle: RePEc:eee:csdana:v:100:y:2016:i:c:p:318-330
    DOI: 10.1016/j.csda.2014.06.012
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    References listed on IDEAS

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    1. Kon, Stanley J, 1984. "Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-165, March.
    2. Jiahua Chen & Pengfei Li & Yuejiao Fu, 2012. "Inference on the Order of a Normal Mixture," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1096-1105, September.
    3. Bulla, Jan & Bulla, Ingo, 2006. "Stylized facts of financial time series and hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2192-2209, December.
    4. Geweke, John & Amisano, Gianni, 2010. "Comparing and evaluating Bayesian predictive distributions of asset returns," International Journal of Forecasting, Elsevier, vol. 26(2), pages 216-230, April.
    5. Mary Hardy, 2001. "A Regime-Switching Model of Long-Term Stock Returns," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 41-53.
    6. Stöber, Jakob & Czado, Claudia, 2014. "Regime switches in the dependence structure of multidimensional financial data," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 672-686.
    7. John Geweke & Gianni Amisano, 2011. "Hierarchical Markov normal mixture models with applications to financial asset returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 1-29, January/F.
    8. Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
    9. Hajo Holzmann & Axel Munk & Tilmann Gneiting, 2006. "Identifiability of Finite Mixtures of Elliptical Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 753-763, December.
    10. Tobias Rydén & Timo Teräsvirta & Stefan Åsbrink, 1998. "Stylized facts of daily return series and the hidden Markov model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(3), pages 217-244.
    11. Bulla, Jan, 2006. "Application of Hidden Markov Models and Hidden Semi-Markov Models to Financial Time Series," MPRA Paper 7675, University Library of Munich, Germany.
    12. Chen, Jiahua & Tan, Xianming, 2009. "Inference for multivariate normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1367-1383, August.
    13. Li, Pengfei & Chen, Jiahua, 2010. "Testing the Order of a Finite Mixture," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1084-1092.
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    Cited by:

    1. Xun Huang & Huiyue Tang, 2022. "Measuring multi‐volatility states of financial markets based on multifractal clustering model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(3), pages 422-434, April.
    2. Guglielmo D'Amico & Ada Lika & Filippo Petroni, 2018. "Indexed Markov Chains for financial data: testing for the number of states of the index process," Papers 1802.01540, arXiv.org.
    3. Guglielmo D’Amico & Ada Lika & Filippo Petroni, 2019. "Change point dynamics for financial data: an indexed Markov chain approach," Annals of Finance, Springer, vol. 15(2), pages 247-266, June.
    4. Geir D. Berentsen & Jan Bulla & Antonello Maruotti & Bård Støve, 2022. "Modelling clusters of corporate defaults: Regime‐switching models significantly reduce the contagion source," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(3), pages 698-722, June.

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