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Penalized estimation of flexible hidden Markov models for time series of counts

Author

Listed:
  • Timo Adam

    (Bielefeld University)

  • Roland Langrock

    (Bielefeld University)

  • Christian H. Weiß

    (Helmut-Schmidt-University Hamburg)

Abstract

We propose an effectively nonparametric approach to fitting hidden Markov models to time series of counts, where the state-dependent distributions are estimated in a completely data-driven way without the need to specify a parametric family of distributions. To avoid overfitting, a roughness penalty based on higher-order differences between adjacent count probabilities is added to the likelihood, which is demonstrated to produce smooth state-dependent probability mass functions. The feasibility of the suggested approach is assessed in simulation experiments, and further illustrated in two real-data applications, where we model the distributions of (i) major earthquake counts and (ii) acceleration counts of an oceanic whitetip shark (Carcharhinus longimanus) over time. The proposed methodology is implemented in the accompanying R package countHMM, which is available on CRAN.

Suggested Citation

  • Timo Adam & Roland Langrock & Christian H. Weiß, 2019. "Penalized estimation of flexible hidden Markov models for time series of counts," METRON, Springer;Sapienza Università di Roma, vol. 77(2), pages 87-104, August.
    • Handle: RePEc:spr:metron:v:77:y:2019:i:2:d:10.1007_s40300-019-00153-6
    DOI: 10.1007/s40300-019-00153-6
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    References listed on IDEAS

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    1. Roland Langrock & Thomas Kneib & Alexander Sohn & Stacy L. DeRuiter, 2015. "Nonparametric inference in hidden Markov models using P-splines," Biometrics, The International Biometric Society, vol. 71(2), pages 520-528, June.
    2. Gordon Anderson & Alessio Farcomeni & Maria Grazia Pittau & Roberto Zelli, 2019. "Rectangular latent Markov models for time‐specific clustering, with an analysis of the wellbeing of nations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 68(3), pages 603-621, April.
    3. Jennifer Pohle & Roland Langrock & Floris M. Beest & Niels Martin Schmidt, 2017. "Selecting the Number of States in Hidden Markov Models: Pragmatic Solutions Illustrated Using Animal Movement," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 270-293, September.
    4. Francesco Lagona & Antonello Maruotti & Fabio Padovano, 2015. "Multilevel multivariate modelling of legislative count data, with a hidden Markov chain," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 705-723, June.
    5. G. Alexandrovich & H. Holzmann & A. Leister, 2016. "Nonparametric identification and maximum likelihood estimation for hidden Markov models," Biometrika, Biometrika Trust, vol. 103(2), pages 423-434.
    6. J. Hambuckers & T. Kneib & R. Langrock & A. Silbersdorff, 2018. "A Markov-switching generalized additive model for compound Poisson processes, with applications to operational loss models," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1679-1698, October.
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    Citations

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    Cited by:

    1. Maxime Faymonville & Carsten Jentsch & Christian H. Weiß & Boris Aleksandrov, 2023. "Semiparametric estimation of INAR models using roughness penalization," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 365-400, June.
    2. Jan Bulla & Roland Langrock & Antonello Maruotti, 2019. "Guest editor’s introduction to the special issue on “Hidden Markov Models: Theory and Applications”," METRON, Springer;Sapienza Università di Roma, vol. 77(2), pages 63-66, August.
    3. 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).
    4. Morteza Amini & Afarin Bayat & Reza Salehian, 2023. "hhsmm: an R package for hidden hybrid Markov/semi-Markov models," Computational Statistics, Springer, vol. 38(3), pages 1283-1335, September.

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