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Maximum spacing estimation for hidden Markov models

Author

Listed:
  • Kristi Kuljus

    (University of Tartu)

  • Bo Ranneby

    (Swedish University of Agricultural Sciences)

Abstract

This article generalizes the maximum spacing (MSP) method to dependent observations by considering hidden Markov models. The MSP method for estimating the model parameters is applied in two steps: at first the parameters of the marginal distribution of observations are estimated, in the second step the transition probabilities of the underlying Markov chain are estimated using the obtained marginal parameter estimates. We prove that the proposed MSP estimation procedure gives consistent estimators. The possibility of using the proposed estimation procedure in the context of model validation is investigated in simulation examples. It is demonstrated that when the observations are dependent, then taking into account the dependence structure by considering two-dimensional spacings provides additional information about a suitable number of mixture components in the model. The proposed estimation method is also applied in a real data example.

Suggested Citation

  • Kristi Kuljus & Bo Ranneby, 2025. "Maximum spacing estimation for hidden Markov models," Statistical Inference for Stochastic Processes, Springer, vol. 28(1), pages 1-31, April.
    • Handle: RePEc:spr:sistpr:v:28:y:2025:i:1:d:10.1007_s11203-025-09325-w
    DOI: 10.1007/s11203-025-09325-w
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    References listed on IDEAS

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    1. Liu, Zhenya & Wang, Shixuan, 2017. "Decoding Chinese stock market returns: Three-state hidden semi-Markov model," Pacific-Basin Finance Journal, Elsevier, vol. 44(C), pages 127-149.
    2. Kristi Kuljus & Bo Ranneby, 2021. "Maximum spacing estimation for continuous time Markov chains and semi-Markov processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 421-443, July.
    3. M. Ekström & S. M. Mirakhmedov & S. Rao Jammalamadaka, 2020. "A class of asymptotically efficient estimators based on sample spacings," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 617-636, September.
    4. Kristi Kuljus & Bo Ranneby, 2015. "Generalized Maximum Spacing Estimation for Multivariate Observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1092-1108, December.
    5. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    6. Kristi Kuljus & Bo Ranneby, 2020. "Asymptotic normality of generalized maximum spacing estimators for multivariate observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 968-989, September.
    7. Rahul Singh & Neeraj Misra, 2023. "A class of estimators based on overlapping sample spacings," Statistical Papers, Springer, vol. 64(6), pages 2137-2160, December.
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