IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i11p3835-3861.html
   My bibliography  Save this article

Uniform time average consistency of Monte Carlo particle filters

Author

Listed:
  • van Handel, Ramon

Abstract

We prove that bootstrap-type Monte Carlo particle filters approximate the optimal nonlinear filter in a time average sense uniformly with respect to the time horizon when the signal is ergodic and the particle system satisfies a tightness property. The latter is satisfied without further assumptions when the signal state space is compact, as well as in the noncompact setting when the signal is geometrically ergodic and the observations satisfy additional regularity assumptions.

Suggested Citation

  • van Handel, Ramon, 2009. "Uniform time average consistency of Monte Carlo particle filters," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3835-3861, November.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:11:p:3835-3861
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(09)00155-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Olsson, Jimmy & Rydén, Tobias, 2008. "Asymptotic properties of particle filter-based maximum likelihood estimators for state space models," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 649-680, April.
    3. LeGland, François & Oudjane, Nadia, 2003. "A robustification approach to stability and to uniform particle approximation of nonlinear filters: the example of pseudo-mixing signals," Stochastic Processes and their Applications, Elsevier, vol. 106(2), pages 279-316, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Laurent-Emmanuel Calvet & Veronika Czellar, 2011. "State-Observation Sampling and the Econometrics of Learning Models," Working Papers hal-00625500, HAL.
    2. Whiteley, Nick & Kantas, Nikolas & Jasra, Ajay, 2012. "Linear variance bounds for particle approximations of time-homogeneous Feynman–Kac formulae," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1840-1865.
    3. Calvet, Laurent E. & Czellar, Veronika, 2015. "Through the looking glass: Indirect inference via simple equilibria," Journal of Econometrics, Elsevier, vol. 185(2), pages 343-358.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wen Xu, 2016. "Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters," Econometrics, MDPI, vol. 4(4), pages 1-13, October.
    2. Laruelle Sophie & Pagès Gilles, 2012. "Stochastic approximation with averaging innovation applied to Finance," Monte Carlo Methods and Applications, De Gruyter, vol. 18(1), pages 1-51, January.
    3. Zhiqiang Li & Jie Xiong, 2015. "Stability of the filter with Poisson observations," Statistical Inference for Stochastic Processes, Springer, vol. 18(3), pages 293-313, October.
    4. Hanming Fang & Edward Kung, 2021. "Why do life insurance policyholders lapse? The roles of income, health, and bequest motive shocks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(4), pages 937-970, December.
    5. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    6. Jiawen Xu & Pierre Perron, 2023. "Forecasting in the presence of in-sample and out-of-sample breaks," Empirical Economics, Springer, vol. 64(6), pages 3001-3035, June.
    7. Kristensen, Dennis & Salanié, Bernard, 2017. "Higher-order properties of approximate estimators," Journal of Econometrics, Elsevier, vol. 198(2), pages 189-208.
    8. Jiawen Xu & Pierre Perron, 2015. "Forecasting in the presence of in and out of sample breaks," Boston University - Department of Economics - Working Papers Series wp2015-012, Boston University - Department of Economics.
    9. Vila, Jean-Pierre, 2012. "Enhanced consistency of the Resampled Convolution Particle Filter," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 786-797.
    10. Jiawen Xu & Pierre Perron, 2015. "Forecasting in the presence of in and out of sample breaks," Boston University - Department of Economics - Working Papers Series wp2015-012, Boston University - Department of Economics.
    11. Travers, Nicholas F., 2014. "Exponential bounds for convergence of entropy rate approximations in hidden Markov models satisfying a path-mergeability condition," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4149-4170.
    12. Whiteley, Nick, 2021. "Dimension-free Wasserstein contraction of nonlinear filters," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 31-50.
    13. Jacob, Pierre E., 2012. "Contributions computationnelles à la statistique Bayésienne," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/12804 edited by Robert, Christian P..
    14. 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.
    15. Nick Whiteley & Nikolas Kantas, 2017. "Calculating Principal Eigen-Functions of Non-Negative Integral Kernels: Particle Approximations and Applications," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1007-1034, November.
    16. Lux, Thomas, 2018. "Estimation of agent-based models using sequential Monte Carlo methods," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 391-408.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:119:y:2009:i:11:p:3835-3861. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.