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Practical filtering with sequential parameter learning

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

Abstract

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. Copyright (c) 2008 The Authors.

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.
  • Handle: RePEc:bla:jorssb:v:70:y:2008:i:2:p:413-428
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    File URL: http://www.blackwell-synergy.com/doi/abs/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," The Warwick Economics Research Paper Series (TWERPS) 651, University of Warwick, Department of Economics.
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    Cited by:

    1. repec:eee:reensy:v:113:y:2013:i:c:p:7-20 is not listed on IDEAS
    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. 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.
    4. Malik, Sheheryar & Pitt, Michael K., 2011. "Particle filters for continuous likelihood evaluation and maximisation," Journal of Econometrics, Elsevier, vol. 165(2), pages 190-209.
    5. Karol Gellert & Erik Schlögl, 2018. "Parameter Learning and Change Detection Using a Particle Filter With Accelerated Adaptation," Research Paper Series 392, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Laurent-Emmanuel Calvet & Veronika Czellar, 2011. "State-Observation Sampling and the Econometrics of Learning Models," Working Papers hal-00625500, HAL.
    7. 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.
    8. Creal, D., 2009. "A survey of sequential Monte Carlo methods for economics and finance," Serie Research Memoranda 0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    9. 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.
    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. Karol Gellert & Erik Schlogl, 2018. "Parameter Learning and Change Detection Using a Particle Filter With Accelerated Adaptation," Papers 1806.05387, arXiv.org.

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