IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v109y2025i2d10.1007_s10182-024-00514-1.html
   My bibliography  Save this article

Hidden-Markov models for ordinal time series

Author

Listed:
  • Christian H. Weiß

    (Helmut Schmidt University)

  • Osama Swidan

    (Helmut Schmidt University)

Abstract

A common approach for modeling categorical time series is Hidden-Markov models (HMMs), where the actual observations are assumed to depend on hidden states in their behavior and transitions. Such categorical HMMs are even applicable to nominal data but suffer from a large number of model parameters. In the ordinal case, however, the natural order among the categorical outcomes offers the potential to reduce the number of parameters while improving their interpretability at the same time. The class of ordinal HMMs proposed in this article link a latent-variable approach with categorical HMMs. They are characterized by parametric parsimony and allow the easy calculation of relevant stochastic properties, such as marginal and bivariate probabilities. These points are illustrated by numerical examples and simulation experiments, where the performance of maximum likelihood estimation is analyzed in finite samples. The developed methodology is applied to real-world data from a health application.

Suggested Citation

  • Christian H. Weiß & Osama Swidan, 2025. "Hidden-Markov models for ordinal time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 109(2), pages 217-239, June.
    • Handle: RePEc:spr:alstar:v:109:y:2025:i:2:d:10.1007_s10182-024-00514-1
    DOI: 10.1007/s10182-024-00514-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-024-00514-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10182-024-00514-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Iain L. MacDonald, 2021. "Is EM really necessary here? Examples where it seems simpler not to use EM," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 629-647, December.
    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. Iain L. MacDonald, 2014. "Numerical Maximisation of Likelihood: A Neglected Alternative to EM?," International Statistical Review, International Statistical Institute, vol. 82(2), pages 296-308, August.
    4. Mengya Liu & Fukang Zhu & Ke Zhu, 2022. "Modeling normalcy‐dominant ordinal time series: An application to air quality level," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 460-478, May.
    5. Jan Bulla & Andreas Berzel, 2008. "Computational issues in parameter estimation for stationary hidden Markov models," Computational Statistics, Springer, vol. 23(1), pages 1-18, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shi, Yue & Punzo, Antonio & Otneim, Håkon & Maruotti, Antonello, 2025. "Hidden semi-Markov models for rainfall-related insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 91-106.
    2. 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.
    3. Maruotti, Antonello & Petrella, Lea & Sposito, Luca, 2021. "Hidden semi-Markov-switching quantile regression for time series," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    4. 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.
    5. Roland Langrock & Timo Adam & Vianey Leos‐Barajas & Sina Mews & David L. Miller & Yannis P. Papastamatiou, 2018. "Spline‐based nonparametric inference in general state‐switching models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 179-200, August.
    6. Maruotti, Antonello & Punzo, Antonio, 2017. "Model-based time-varying clustering of multivariate longitudinal data with covariates and outliers," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 475-496.
    7. Antonello Maruotti, 2015. "Handling non-ignorable dropouts in longitudinal data: a conditional model based on a latent Markov heterogeneity structure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 84-109, March.
    8. Bulla, Jan & Mergner, Sascha & Bulla, Ingo & Sesboüé, André & Chesneau, Christophe, 2010. "Markov-switching Asset Allocation: Do Profitable Strategies Exist?," MPRA Paper 21154, University Library of Munich, Germany.
    9. Jan Bulla, 2010. "Hidden Markov models with t components. Increased persistence and other aspects," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 459-475.
    10. Iain L. MacDonald & Brendon M. Lapham, 2016. "Even More Direct Calculation of the Variance of a Maximum Penalized-Likelihood Estimator," The American Statistician, Taylor & Francis Journals, vol. 70(1), pages 114-118, February.
    11. Mark, Tanya & Bulla, Jan & Niraj, Rakesh & Bulla, Ingo & Schwarzwäller, Wolfgang, 2019. "Catalogue as a tool for reinforcing habits: Empirical evidence from a multichannel retailer," International Journal of Research in Marketing, Elsevier, vol. 36(4), pages 528-541.
    12. Janczura, Joanna & Weron, Rafal, 2010. "Goodness-of-fit testing for regime-switching models," MPRA Paper 22871, University Library of Munich, Germany.
    13. 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.
    14. Shi, Yue & Punzo, Antonio & Otneim, Håkon & Maruotti, Antonello, 2023. "Hidden semi-Markov models for rainfall-related insurance claims," Discussion Papers 2023/17, Norwegian School of Economics, Department of Business and Management Science.
    15. Kristian Gundersen & Timothée Bacri & Jan Bulla & Sondre Hølleland & Antonello Maruotti & Bård Støve, 2024. "Testing for time‐varying nonlinear dependence structures: Regime‐switching and local Gaussian correlation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1012-1060, September.
    16. Lanyu Xiong & Fukang Zhu, 2024. "Robust estimation for the one-parameter exponential family integer-valued GARCH(1,1) models based on a modified Tukey’s biweight function," Computational Statistics, Springer, vol. 39(2), pages 495-522, April.
    17. 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.
    18. Iain L. MacDonald, 2014. "Numerical Maximisation of Likelihood: A Neglected Alternative to EM?," International Statistical Review, International Statistical Institute, vol. 82(2), pages 296-308, August.
    19. Gordon Anderson & Alessio Farcomeni & Grazia Pittau & Roberto Zelli, 2017. "Rectangular latent Markov models for time-specific clustering," Working Papers tecipa-589, University of Toronto, Department of Economics.
    20. Huaping Chen, 2023. "A New Soft-Clipping Discrete Beta GARCH Model and Its Application on Measles Infection," Stats, MDPI, vol. 6(1), pages 1-19, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:alstar:v:109:y:2025:i:2:d:10.1007_s10182-024-00514-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.