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Practical filtering with sequential parameter learning

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  • Nicholas G. Polson
  • Jonathan R. Stroud
  • Peter Müller

Abstract

Summary. The paper develops a simulation‐based approach to sequential parameter learning and filtering in general state space models. Our approach is based on approximating the target posterior by a mixture of fixed lag smoothing distributions. Parameter inference exploits a sufficient statistic structure and the methodology can be easily implemented by modifying state space smoothing algorithms. We avoid reweighting particles and hence sample degeneracy problems that plague particle filters that use sequential importance sampling. The method is illustrated by using two examples: a benchmark auto‐regressive model with observation error and a high dimensional dynamic spatiotemporal model. We show that the method provides accurate inference in the presence of outliers, model misspecification and high dimensionality.

Suggested Citation

  • Nicholas G. Polson & Jonathan R. Stroud & Peter Müller, 2008. "Practical filtering with sequential parameter learning," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 413-428, April.
  • Handle: RePEc:bla:jorssb:v:70:y:2008:i:2:p:413-428
    DOI: 10.1111/j.1467-9868.2007.00642.x
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    References listed on IDEAS

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    1. Pitt, Michael K., 2002. "Smooth particle filters for likelihood evaluation and maximisation," Economic Research Papers 269464, University of Warwick - Department of Economics.
    2. Pitt, Michael K, 2002. "Smooth Particle Filters for Likelihood Evaluation and Maximisation," The Warwick Economics Research Paper Series (TWERPS) 651, University of Warwick, Department of Economics.
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    Cited by:

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    2. Kostas Triantafyllopoulos, 2009. "Inference of Dynamic Generalized Linear Models: On‐Line Computation and Appraisal," International Statistical Review, International Statistical Institute, vol. 77(3), pages 430-450, December.
    3. Malik, Sheheryar & Pitt, Michael K., 2011. "Particle filters for continuous likelihood evaluation and maximisation," Journal of Econometrics, Elsevier, vol. 165(2), pages 190-209.
    4. Laurent-Emmanuel Calvet & Veronika Czellar, 2011. "State-Observation Sampling and the Econometrics of Learning Models," Working Papers hal-00625500, HAL.
    5. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    6. Drew Creal, 2012. "A Survey of Sequential Monte Carlo Methods for Economics and Finance," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 245-296.
    7. He, Zhongfang & Maheu, John M., 2010. "Real time detection of structural breaks in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2628-2640, November.
    8. Karol Gellert & Erik Schlögl, 2021. "Parameter Learning and Change Detection Using a Particle Filter with Accelerated Adaptation," Risks, MDPI, vol. 9(12), pages 1-18, December.
    9. Rutger Jan Lange, 2020. "Bellman filtering for state-space models," Tinbergen Institute Discussion Papers 20-052/III, Tinbergen Institute, revised 19 May 2021.
    10. Naoki Awaya & Yasuhiro Omori, 2017. "Particle rolling MCMC with Double Block Sampling: Conditional SMC Update Approach," CIRJE F-Series CIRJE-F-1066, CIRJE, Faculty of Economics, University of Tokyo.
    11. Kenichiro McAlinn & Asahi Ushio & Teruo Nakatsuma, 2016. "Volatility Forecasts Using Nonlinear Leverage Effects," Papers 1605.06482, arXiv.org, revised Dec 2017.
    12. Jin, Guang & Matthews, David E. & Zhou, Zhongbao, 2013. "A Bayesian framework for on-line degradation assessment and residual life prediction of secondary batteries inspacecraft," Reliability Engineering and System Safety, Elsevier, vol. 113(C), pages 7-20.
    13. Ren-Her Wang & John Aston & Cheng-Der Fuh, 2010. "The Role of Additional Information in Option Pricing: Estimation Issues for the State Space Model," Computational Economics, Springer;Society for Computational Economics, vol. 36(4), pages 283-307, December.
    14. Turnbull, Kathryn & Nemeth, Christopher & Nunes, Matthew & McCormick, Tyler, 2023. "Sequential estimation of temporally evolving latent space network models," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    15. Pierre Del Moral & Ajay Jasra & Yan Zhou, 2017. "Biased Online Parameter Inference for State-Space Models," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 727-749, September.
    16. Naoki Awaya & Yasuhiro Omori, 2019. "Particle rolling MCMC," CIRJE F-Series CIRJE-F-1110, CIRJE, Faculty of Economics, University of Tokyo.

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