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


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  • Dembo, A.
  • Zeitouni, O.
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 23 (1986)
    Issue (Month): 1 (October)
    Pages: 91-113

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    Handle: RePEc:eee:spapps:v:23:y:1986:i:1:p:91-113

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    Keywords: parameter estimation EM algorithm maximum likelihood diffusion processes non-linear smoothing ARMA processes;


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    Cited by:
    1. 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.
    2. 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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