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A note on auxiliary particle filters

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  • Johansen, Adam M.
  • Doucet, Arnaud

Abstract

The auxiliary particle filter (APF) introduced by Pitt and Shephard [Pitt, M.K., Shephard, N., 1999. Filtering via simulation: Auxiliary particle filters. J. Am. Statist. Ass. 94, 590-599] is a very popular alternative to Sequential Importance Sampling and Resampling (SISR) algorithms to perform inference in state-space models. We propose a novel interpretation of the APFÂ as an SISRÂ algorithm. This interpretation allows us to present simple guidelines to ensure good performance of the APF and the first convergence results for this algorithm. Additionally, we show that, contrary to popular belief, the asymptotic variance of APF-based estimators is not always smaller than those of the corresponding SISR estimators -- even in the 'perfect adaptation' scenario.

Suggested Citation

  • Johansen, Adam M. & Doucet, Arnaud, 2008. "A note on auxiliary particle filters," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1498-1504, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:12:p:1498-1504
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    References listed on IDEAS

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    1. 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.
    2. Paul Fearnhead & Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Particle filters for partially observed diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 755-777, September.
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    Cited by:

    1. Maciej Augustyniak & Mathieu Boudreault & Manuel Morales, 2018. "Maximum Likelihood Estimation of the Markov-Switching GARCH Model Based on a General Collapsing Procedure," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 165-188, March.
    2. Crucinio, Francesca R. & Johansen, Adam M., 2023. "Properties of marginal sequential Monte Carlo methods," Statistics & Probability Letters, Elsevier, vol. 203(C).
    3. Elmar Mertens & James M. Nason, 2020. "Inflation and professional forecast dynamics: An evaluation of stickiness, persistence, and volatility," Quantitative Economics, Econometric Society, vol. 11(4), pages 1485-1520, November.
    4. Axel Finke & Adam Johansen & Dario Spanò, 2014. "Static-parameter estimation in piecewise deterministic processes using particle Gibbs samplers," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 577-609, June.
    5. Audronė Virbickaitė & Hedibert F. Lopes & M. Concepción Ausín & Pedro Galeano, 2019. "Particle learning for Bayesian semi-parametric stochastic volatility model," Econometric Reviews, Taylor & Francis Journals, vol. 38(9), pages 1007-1023, October.
    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. Murray Pollock & Paul Fearnhead & Adam M. Johansen & Gareth O. Roberts, 2020. "Quasi‐stationary Monte Carlo and the ScaLE algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1167-1221, December.
    8. Yang, Yuan & Wang, Lu, 2015. "An Improved Auxiliary Particle Filter for Nonlinear Dynamic Equilibrium Models," Dynare Working Papers 47, CEPREMAP.

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