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Parameter estimation of partially observed continuous time stochastic processes via the EM algorithm

Author

Listed:
  • Dembo, A.
  • Zeitouni, O.

Abstract

An algorithm is presented for the problem of maximum likelihood (ML) estimation of parameters of partially observed continuous time random processes. This algorithm is an extension of the EM algorithm [3] used in the time series literature, and preserves its main features. It is then applied to the problem of parameter estimation of continuous time, finite state or infinite state (diffusions) Markov processes observed via a noisy sensor. The algorithm in general involves iterations of non-linear smoothing with known parameters and then a non-stochastic maximization. For special cases, including linear models and AR/ARMA processes observed in white noise, each iteration is easily performed with finite dimensional filters. Finally, the algorithm is applied to parameter estimation of "randomly slowly varying" linear systems observed in white noise, and explicit results are derived.

Suggested Citation

  • Dembo, A. & Zeitouni, O., 1986. "Parameter estimation of partially observed continuous time stochastic processes via the EM algorithm," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 91-113, October.
    • Handle: RePEc:eee:spapps:v:23:y:1986:i:1:p:91-113
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    Citations

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    Cited by:

    1. Masaaki Fukasawa, 2021. "EM algorithm for stochastic hybrid systems," Statistical Inference for Stochastic Processes, Springer, vol. 24(1), pages 223-239, April.
    2. Robert Elliott & Eckhard Platen, 1999. "Hidden Markov Chain Filtering for Generalised Bessel Processes," Research Paper Series 23, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Elliott Robert J. & Siu Tak Kuen & Lau John W., 2018. "A hidden Markov regime-switching smooth transition model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(4), pages 1-21, September.
    4. Sy-Miin Chow & Zhaohua Lu & Andrew Sherwood & Hongtu Zhu, 2016. "Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation–Maximization (SAEM) Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 102-134, March.
    5. Damian Camilla & Eksi Zehra & Frey Rüdiger, 2018. "EM algorithm for Markov chains observed via Gaussian noise and point process information: Theory and case studies," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 51-72, January.
    6. Elliott, Robert J. & Siu, Tak Kuen & Badescu, Alex, 2010. "On mean-variance portfolio selection under a hidden Markovian regime-switching model," Economic Modelling, Elsevier, vol. 27(3), pages 678-686, May.
    7. Elliott, R. J. & Malcolm, W. P. & Tsoi, Allanus H., 2003. "Robust parameter estimation for asset price models with Markov modulated volatilities," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1391-1409, June.

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