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Particle-based online estimation of tangent filters with application to parameter estimation in nonlinear state-space models

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  • Jimmy Olsson

    (KTH Royal Institute of Technology)

  • Johan Westerborn Alenlöv

    (KTH Royal Institute of Technology)

Abstract

This paper presents a novel algorithm for efficient online estimation of the filter derivatives in general hidden Markov models. The algorithm, which has a linear computational complexity and very limited memory requirements, is furnished with a number of convergence results, including a central limit theorem with an asymptotic variance that can be shown to be uniformly bounded in time. Using the proposed filter derivative estimator, we design a recursive maximum likelihood algorithm updating the parameters according the gradient of the one-step predictor log-likelihood. The efficiency of this online parameter estimation scheme is illustrated in a simulation study.

Suggested Citation

  • Jimmy Olsson & Johan Westerborn Alenlöv, 2020. "Particle-based online estimation of tangent filters with application to parameter estimation in nonlinear state-space models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 545-576, April.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:2:d:10.1007_s10463-018-0698-1
    DOI: 10.1007/s10463-018-0698-1
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    References listed on IDEAS

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    1. Arnaud Doucet & Vladislav Tadić, 2003. "Parameter estimation in general state-space models using particle methods," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 409-422, June.
    2. George Poyiadjis & Arnaud Doucet & Sumeetpal S. Singh, 2011. "Particle approximations of the score and observed information matrix in state space models with application to parameter estimation," Biometrika, Biometrika Trust, vol. 98(1), pages 65-80.
    3. Paul Fearnhead & David Wyncoll & Jonathan Tawn, 2010. "A sequential smoothing algorithm with linear computational cost," Biometrika, Biometrika Trust, vol. 97(2), pages 447-464.
    4. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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