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Hidden Markov models with arbitrary state dwell-time distributions

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  • Langrock, R.
  • Zucchini, W.

Abstract

A hidden Markov model (HMM) with a special structure that captures the 'semi'-property of hidden semi-Markov models (HSMMs) is considered. The proposed model allows arbitrary dwell-time distributions in the states of the Markov chain. For dwell-time distributions with finite support the HMM formulation is exact while for those that have infinite support, e.g. the Poisson, the distribution can be approximated with arbitrary accuracy. A benefit of using the HMM formulation is that it is easy to incorporate covariates, trend and seasonal variation particularly in the hidden component of the model. In addition, the formulae and methods for forecasting, state prediction, decoding and model checking that exist for ordinary HMMs are applicable to the proposed class of models. An HMM with explicitly modeled dwell-time distributions involving seasonality is used to model daily rainfall occurrence for sites in Bulgaria.

Suggested Citation

  • Langrock, R. & Zucchini, W., 2011. "Hidden Markov models with arbitrary state dwell-time distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 715-724, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:715-724
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    References listed on IDEAS

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    1. Altman, Rachel MacKay, 2007. "Mixed Hidden Markov Models: An Extension of the Hidden Markov Model to the Longitudinal Data Setting," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 201-210, March.
    2. Guedon, Yann, 2005. "Hidden hybrid Markov/semi-Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 663-688, June.
    3. Florence Chaubert-Pereira & Yann Guédon & Christian Lavergne & Catherine Trottier, 2010. "Markov and Semi-Markov Switching Linear Mixed Models Used to Identify Forest Tree Growth Components," Biometrics, The International Biometric Society, vol. 66(3), pages 753-762, September.
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    4. Pohle, Jennifer & Adam, Timo & Beumer, Larissa T., 2022. "Flexible estimation of the state dwell-time distribution in hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
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    7. D. L. Borchers & W. Zucchini & M. P. Heide-Jørgensen & A. Cañadas & R. Langrock, 2013. "Using Hidden Markov Models to Deal with Availability Bias on Line Transect Surveys," Biometrics, The International Biometric Society, vol. 69(3), pages 703-713, September.
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