IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v35y2008i2p309-321.html
   My bibliography  Save this article

Likelihood Ratio Testing for Hidden Markov Models Under Non‐standard Conditions

Author

Listed:
  • JÖRN DANNEMANN
  • HAJO HOLZMANN

Abstract

. In practical applications, when testing parametric restrictions for hidden Markov models (HMMs), one frequently encounters non‐standard situations such as testing for zero entries in the transition matrix, one‐sided tests for the parameters of the transition matrix or for the components of the stationary distribution of the underlying Markov chain, or testing boundary restrictions on the parameters of the state‐dependent distributions. In this paper, we briefly discuss how the relevant asymptotic distribution theory for the likelihood ratio test (LRT) when the true parameter is on the boundary extends from the independent and identically distributed situation to HMMs. Then we concentrate on discussing a number of relevant examples. The finite‐sample performance of the LRT in such situations is investigated in a simulation study. An application to series of epileptic seizure counts concludes the paper.

Suggested Citation

  • Jörn Dannemann & Hajo Holzmann, 2008. "Likelihood Ratio Testing for Hidden Markov Models Under Non‐standard Conditions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 309-321, June.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:2:p:309-321
    DOI: 10.1111/j.1467-9469.2007.00587.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9469.2007.00587.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9469.2007.00587.x?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
    ---><---

    References listed on IDEAS

    as
    1. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    2. Tobias Rydén & Timo Teräsvirta & Stefan Åsbrink, 1998. "Stylized facts of daily return series and the hidden Markov model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(3), pages 217-244.
    3. Paolo Giudici & Tobias Ryden & Pierre Vandekerkhove, 2000. "Likelihood-Ratio Tests for Hidden Markov Models," Biometrics, The International Biometric Society, vol. 56(3), pages 742-747, September.
    4. Francesco Bartolucci, 2006. "Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 155-178, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bolano, Danilo & Berchtold, André, 2016. "General framework and model building in the class of Hidden Mixture Transition Distribution models," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 131-145.
    2. Ray, Surajit & Ren, Dan, 2012. "On the upper bound of the number of modes of a multivariate normal mixture," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 41-52.

    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. Dannemann, Jorn & Holzmann, Hajo, 2008. "The likelihood ratio test for hidden Markov models in two-sample problems," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1850-1859, January.
    2. Paolo Giudici & Tobias Ryden & Pierre Vandekerkhove, 2000. "Likelihood-Ratio Tests for Hidden Markov Models," Biometrics, The International Biometric Society, vol. 56(3), pages 742-747, September.
    3. Max Greenfeld & Dmitri S Pavlichin & Hideo Mabuchi & Daniel Herschlag, 2012. "Single Molecule Analysis Research Tool (SMART): An Integrated Approach for Analyzing Single Molecule Data," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-12, February.
    4. Rachel MacKay Altman, 2004. "Assessing the Goodness-of-Fit of Hidden Markov Models," Biometrics, The International Biometric Society, vol. 60(2), pages 444-450, June.
    5. Milan Kumar Das & Anindya Goswami, 2019. "Testing of binary regime switching models using squeeze duration analysis," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-20, March.
    6. Ngene, Geoffrey & Tah, Kenneth A. & Darrat, Ali F., 2017. "Long memory or structural breaks: Some evidence for African stock markets," Review of Financial Economics, Elsevier, vol. 34(C), pages 61-73.
    7. Meenagh, David & Minford, Patrick & Peel, David, 2007. "Simulating stock returns under switching regimes - A new test of market efficiency," Economics Letters, Elsevier, vol. 94(2), pages 235-239, February.
    8. Krämer, Walter & Sibbertsen, Philipp & Kleiber, Christian, 2001. "Long memory vs. structural change in financial time series," Technical Reports 2001,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    9. Gil-Alana, L.A., 2006. "Fractional integration in daily stock market indexes," Review of Financial Economics, Elsevier, vol. 15(1), pages 28-48.
    10. María Luz Gámiz & Nikolaos Limnios & Mari Carmen Segovia-García, 2023. "The continuous-time hidden Markov model based on discretization. Properties of estimators and applications," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 525-550, October.
    11. Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
    12. Krishnamurthy, Vikram & Leoff, Elisabeth & Sass, Jörn, 2018. "Filterbased stochastic volatility in continuous-time hidden Markov models," Econometrics and Statistics, Elsevier, vol. 6(C), pages 1-21.
    13. Holzmann, Hajo & Schwaiger, Florian, 2016. "Testing for the number of states in hidden Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 318-330.
    14. Yizhan Shu & Chenyu Yu & John M. Mulvey, 2024. "Downside Risk Reduction Using Regime-Switching Signals: A Statistical Jump Model Approach," Papers 2402.05272, arXiv.org, revised Sep 2024.
    15. Francesco Bartolucci & Ivonne Solis-Trapala, 2010. "Multidimensional Latent Markov Models in a Developmental Study of Inhibitory Control and Attentional Flexibility in Early Childhood," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 725-743, December.
    16. 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.
    17. Ahmed Belhadjayed & Grégoire Loeper & Frédéric Abergel, 2016. "Forecasting Trends With Asset Prices," Post-Print hal-01512431, HAL.
    18. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2020. "On an integer-valued stochastic intensity model for time series of counts," MPRA Paper 105406, University Library of Munich, Germany.
    19. Balcılar, Mehmet & Demirer, Rıza & Hammoudeh, Shawkat, 2015. "Regional and global spillovers and diversification opportunities in the GCC equity sectors," Emerging Markets Review, Elsevier, vol. 24(C), pages 160-187.
    20. Cheung, Yin-Wong & Erlandsson, Ulf G., 2005. "Exchange Rates and Markov Switching Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 314-320, July.

    More about this item

    Statistics

    Access and download statistics

    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:bla:scjsta:v:35:y:2008:i:2:p:309-321. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.