IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v140y2015icp19-30.html
   My bibliography  Save this article

Multiple hidden Markov models for categorical time series

Author

Listed:
  • Colombi, R.
  • Giordano, S.

Abstract

We introduce multiple hidden Markov models (MHMMs) where a multivariate categorical time series depends on a latent multivariate Markov chain. MHMMs provide an elegant framework for specifying various independence relationships between multiple discrete time processes. These independencies are interpreted as Markov properties of a mixed graph and a chain graph associated respectively to the latent and observation components of the MHMM. These Markov properties are also translated into zero restrictions on the parameters of marginal models for the transition probabilities and the distributions of observable variables given the latent states.

Suggested Citation

  • Colombi, R. & Giordano, S., 2015. "Multiple hidden Markov models for categorical time series," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 19-30.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:19-30
    DOI: 10.1016/j.jmva.2015.04.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X15000901
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2015.04.002?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. Thomas Richardson, 2003. "Markov Properties for Acyclic Directed Mixed Graphs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 145-157, March.
    2. Colombi, R. & Giordano, S., 2012. "Graphical models for multivariate Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 90-103.
    3. Gilles Celeux & Jean-Baptiste Durand, 2008. "Selecting hidden Markov model state number with cross-validated likelihood," Computational Statistics, Springer, vol. 23(4), pages 541-564, October.
    4. Roberto Colombi & Sabrina Giordano, 2011. "Testing lumpability for marginal discrete hidden Markov models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 293-311, September.
    5. Florens, J.P. & Mouchart, M. & Rolin, J.M., 1993. "Noncausality and Marginalization of Markov Processes," Econometric Theory, Cambridge University Press, vol. 9(2), pages 241-262, April.
    6. Chris Sherlock & Tatiana Xifara & Sandra Telfer & Mike Begon, 2013. "A coupled hidden Markov model for disease interactions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 609-627, August.
    7. Colombi, Roberto & Giordano, Sabrina & Cazzaro, Manuela, 2014. "hmmm: An R Package for Hierarchical Multinomial Marginal Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 59(i11).
    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. Colombi, R. & Giordano, S., 2012. "Graphical models for multivariate Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 90-103.
    2. Roberto Colombi & Sabrina Giordano, 2013. "Monotone dependence in graphical models for multivariate Markov chains," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 873-885, October.
    3. Robin J. Evans & Thomas S. Richardson, 2013. "Marginal log-linear parameters for graphical Markov models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 743-768, September.
    4. Michel Mouchart & Renzo Orsi, 2016. "Building a Structural Model: Parameterization and Structurality," Econometrics, MDPI, vol. 4(2), pages 1-16, April.
    5. Simon DeDeo, 2016. "Conflict and Computation on Wikipedia: A Finite-State Machine Analysis of Editor Interactions," Future Internet, MDPI, vol. 8(3), pages 1-23, July.
    6. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    7. MOUCHART, Michel & SAN MARTIN , Ernesto, 1998. "Identification problems in a class of mixture models with an application to the LISREL model," LIDAM Discussion Papers CORE 1998025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Fulvia Pennoni & Francesco Bartolucci & Silvia Pandolfi, 2024. "Variable Selection for Hidden Markov Models with Continuous Variables and Missing Data," Journal of Classification, Springer;The Classification Society, vol. 41(3), pages 568-589, November.
    9. Silvana Tiedemann & Jorge Sanchez Canales & Felix Schur & Raffaele Sgarlato & Lion Hirth & Oliver Ruhnau & Jonas Peters, 2024. "Identifying Elasticities in Autocorrelated Time Series Using Causal Graphs," Papers 2409.15530, arXiv.org.
    10. Lorenza Rossi & Emilio Zanetti Chini, 2016. "Firms’ Dynamics and Business Cycle: New Disaggregated Data," DEM Working Papers Series 123, University of Pavia, Department of Economics and Management.
    11. Monia Lupparelli & Giovanni M. Marchetti & Wicher P. Bergsma, 2009. "Parameterizations and Fitting of Bi‐directed Graph Models to Categorical Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 559-576, September.
    12. Janczura, Joanna & Weron, Rafal, 2010. "Goodness-of-fit testing for regime-switching models," MPRA Paper 22871, University Library of Munich, Germany.
    13. Roberto Colombi & Sabrina Giordano, 2019. "Likelihood-based tests for a class of misspecified finite mixture models for ordinal categorical data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1175-1202, December.
    14. Colombi, Roberto, 2020. "Selection tests for possibly misspecified hierarchical multinomial marginal models," Econometrics and Statistics, Elsevier, vol. 16(C), pages 136-147.
    15. Renault, Eric & Triacca, Umberto, 2015. "Causality and separability," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 1-5.
    16. 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.
    17. Lin, Yong & Huang, Mian, 2025. "Penalized composite likelihood estimation for hidden Markov models with unknown number of states," Statistics & Probability Letters, Elsevier, vol. 216(C).
    18. Alberto Roverato, 2015. "Log-mean Linear Parameterization for Discrete Graphical Models of Marginal Independence and the Analysis of Dichotomizations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 627-648, June.
    19. Boitani, Andrea & Punzo, Chiara, 2019. "Banks’ leverage behaviour in a two-agent new Keynesian model," Journal of Economic Behavior & Organization, Elsevier, vol. 162(C), pages 347-359.
    20. 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.

    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:eee:jmvana:v:140:y:2015:i:c:p:19-30. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.