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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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    3. Adam, Timo & Mayr, Andreas & Kneib, Thomas, 2022. "Gradient boosting in Markov-switching generalized additive models for location, scale, and shape," Econometrics and Statistics, Elsevier, vol. 22(C), pages 3-16.
    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).
    5. Sofia Ruiz-Suarez & Vianey Leos-Barajas & Juan Manuel Morales, 2022. "Hidden Markov and Semi-Markov Models When and Why are These Models Useful for Classifying States in Time Series Data?," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 339-363, June.
    6. Giner, Javier & Zakamulin, Valeriy, 2023. "A regime-switching model of stock returns with momentum and mean reversion," Economic Modelling, Elsevier, vol. 122(C).
    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.
    8. Nicosia, Aurélien & Duchesne, Thierry & Rivest, Louis-Paul & Fortin, Daniel, 2017. "A general hidden state random walk model for animal movement," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 76-95.
    9. Maruotti, Antonello & Petrella, Lea & Sposito, Luca, 2021. "Hidden semi-Markov-switching quantile regression for time series," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    10. Choquet, R. & Guédon, Y. & Besnard, A. & Guillemain, M. & Pradel, R., 2013. "Estimating stop over duration in the presence of trap-effects," Ecological Modelling, Elsevier, vol. 250(C), pages 111-118.
    11. Ting Wang & Jiancang Zhuang & Kazushige Obara & Hiroshi Tsuruoka, 2017. "Hidden Markov modelling of sparse time series from non-volcanic tremor observations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 691-715, August.
    12. Zhou, Jie & Song, Xinyuan & Sun, Liuquan, 2020. "Continuous time hidden Markov model for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    13. Degras, David & Ting, Chee-Ming & Ombao, Hernando, 2022. "Markov-switching state-space models with applications to neuroimaging," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    14. Antonello Maruotti & Antonio Punzo, 2021. "Initialization of Hidden Markov and Semi‐Markov Models: A Critical Evaluation of Several Strategies," International Statistical Review, International Statistical Institute, vol. 89(3), pages 447-480, December.

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