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On recursive estimation for hidden Markov models

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  • Rydén, Tobias

Abstract

Hidden Markov models (HMMs) have during the last decade become a widespread tool for modelling sequences of dependent random variables. In this paper we consider a recursive estimator for HMMs based on the m-dimensional distribution of the process and show that this estimator converges to the set of stationary points of the corresponding Kullback-Leibler information. We also investigate averaging in this recursive scheme and show that conditional on convergence to the true parameter, and provided m is chosen large enough, the averaged estimator is close to optimal.

Suggested Citation

  • Rydén, Tobias, 1997. "On recursive estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 79-96, February.
    • Handle: RePEc:eee:spapps:v:66:y:1997:i:1:p:79-96
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    1. Rainer Schwabe & Harro Walk, 1996. "On a stochastic approximation procedure based on averaging," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 44(1), pages 165-180, December.
    2. Ma, D.-J. & Makowski, A.M. & Shwartz, A., 1990. "Stochastic approximations for finite-state Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 35(1), pages 27-45, June.
    3. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    4. Schwabe, R., 1986. "Strong representation of an adaptive stochastic approximation procedure," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 115-130, October.
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    1. Driffill, John & Sola, Martin & Kenc, Turalay & Spagnolo, Fabio, 2004. "On Model Selection and Markov Switching: A Empirical Examination of Term Structure Models with Regime Shifts," CEPR Discussion Papers 4165, C.E.P.R. Discussion Papers.
    2. Tadić, Vladislav Z.B. & Doucet, Arnaud, 2020. "Stability of optimal filter higher-order derivatives," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4808-4858.
    3. Driffill John & Kenc Turalay & Sola Martin & Spagnolo Fabio, 2009. "The Effects of Different Parameterizations of Markov-Switching in a CIR Model of Bond Pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(1), pages 1-24, March.

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