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Particle filtering for partially observed Gaussian state space models

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  • Christophe Andrieu
  • Arnaud Doucet

Abstract

Summary. Solving Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data has many applications for dynamic models. A large number of algorithms based on particle filtering methods, also known as sequential Monte Carlo algorithms, have recently been proposed to solve these problems. We propose a special particle filtering method which uses random mixtures of normal distributions to represent the posterior distributions of partially observed Gaussian state space models. This algorithm is based on a marginalization idea for improving efficiency and can lead to substantial gains over standard algorithms. It differs from previous algorithms which were only applicable to conditionally linear Gaussian state space models. Computer simulations are carried out to evaluate the performance of the proposed algorithm for dynamic tobit and probit models.

Suggested Citation

  • Christophe Andrieu & Arnaud Doucet, 2002. "Particle filtering for partially observed Gaussian state space models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 827-836, October.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:4:p:827-836
    DOI: 10.1111/1467-9868.00363
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    Cited by:

    1. Nonejad, Nima, 2014. "Particle Gibbs with Ancestor Sampling Methods for Unobserved Component Time Series Models with Heavy Tails, Serial Dependence and Structural Breaks," MPRA Paper 55664, University Library of Munich, Germany.
    2. Mark Briers & Arnaud Doucet & Simon Maskell, 2010. "Smoothing algorithms for state–space models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(1), pages 61-89, February.
    3. Wen Xu, 2016. "Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters," Econometrics, MDPI, vol. 4(4), pages 1-13, October.
    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. N. H. Chan & A. E. Brockwell, 2006. "Long-memory dynamic Tobit models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(5), pages 351-367.
    6. Name 1 Dieter Wang Email 1 & Iman (I.P.P.) van Lelyveld & Julia (J.) Schaumburg, 2018. "Do information contagion and business model similarities explain bank credit risk commonalities?," Tinbergen Institute Discussion Papers 18-100/IV, Tinbergen Institute.
    7. Laurent-Emmanuel Calvet & Veronika Czellar, 2011. "State-Observation Sampling and the Econometrics of Learning Models," Working Papers hal-00625500, HAL.
    8. 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.
    9. Dani Gamerman & Thiago Rezende Santos & Glaura C. Franco, 2013. "A Non-Gaussian Family Of State-Space Models With Exact Marginal Likelihood," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 625-645, November.
    10. Crisan, D. & Li, K., 2015. "Generalised particle filters with Gaussian mixtures," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2643-2673.
    11. Chopin, N. & Del Moral, P. & Rubenthaler, S., 2011. "Stability of Feynman-Kac formulae with path-dependent potentials," Stochastic Processes and their Applications, Elsevier, vol. 121(1), pages 38-60, January.
    12. Nicolas Chopin, 2002. "Central Limit Theorem for Sequential Monte Carlo Methods and its Applications to Bayesian Inference," Working Papers 2002-44, Center for Research in Economics and Statistics.
    13. Nalan Basturk & Cem Cakmakli & S. Pinar Ceyhan & Herman K. van Dijk, 2014. "On the Rise of Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 14-085/III, Tinbergen Institute, revised 04 Sep 2014.
    14. Jian He & Asma Khedher & Peter Spreij, 2021. "A Kalman particle filter for online parameter estimation with applications to affine models," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 353-403, July.
    15. Nonejad Nima, 2015. "Particle Gibbs with ancestor sampling for stochastic volatility models with: heavy tails, in mean effects, leverage, serial dependence and structural breaks," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(5), pages 561-584, December.
    16. Douc, R. & Fort, G. & Moulines, E. & Priouret, P., 2009. "Forgetting the initial distribution for Hidden Markov Models," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1235-1256, April.
    17. 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.
    18. Nonejad, Nima, 2014. "Particle Markov Chain Monte Carlo Techniques of Unobserved Component Time Series Models Using Ox," MPRA Paper 55662, University Library of Munich, Germany.
    19. Nalan Basturk & Cem Cakmakli & S. Pinar Ceyhan & Herman K. van Dijk, 2013. "Historical Developments in Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 13-191/III, Tinbergen Institute.
    20. Pitt, Michael K., 2002. "Smooth particle filters for likelihood evaluation and maximisation," Economic Research Papers 269464, University of Warwick - Department of Economics.
    21. Charles S. Bos & Siem Jan Koopman, 2010. "Models with Time-varying Mean and Variance: A Robust Analysis of U.S. Industrial Production," Tinbergen Institute Discussion Papers 10-017/4, Tinbergen Institute.
    22. Younghoon Kim & Marie-Christine Duker & Zachary F. Fisher & Vladas Pipiras, 2023. "Latent Gaussian dynamic factor modeling and forecasting for multivariate count time series," Papers 2307.10454, arXiv.org, revised Jul 2024.
    23. Papavasiliou, Anastasia, 2006. "Parameter estimation and asymptotic stability in stochastic filtering," Stochastic Processes and their Applications, Elsevier, vol. 116(7), pages 1048-1065, July.
    24. A. E. Brockwell & N. H. Chan & P. K. Lee, 2003. "A class of models for aggregated traffic volume time series," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(4), pages 417-430, October.
    25. Andreas Hetland, 2018. "The Stochastic Stationary Root Model," Econometrics, MDPI, vol. 6(3), pages 1-33, August.

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