IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v121y2011i1p38-60.html
   My bibliography  Save this article

Stability of Feynman-Kac formulae with path-dependent potentials

Author

Listed:
  • Chopin, N.
  • Del Moral, P.
  • Rubenthaler, S.

Abstract

Several particle algorithms admit a Feynman-Kac representation such that the potential function may be expressed as a recursive function which depends on the complete state trajectory. An important example is the mixture Kalman filter, but other models and algorithms of practical interest fall in this category. We study the asymptotic stability of such particle algorithms as time goes to infinity. As a corollary, practical conditions for the stability of the mixture Kalman filter, and a mixture GARCH filter, are derived. Finally, we show that our results can also lead to weaker conditions for the stability of standard particle algorithms for which the potential function depends on the last state only.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:1:p:38-60
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(10)00221-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Rong Chen & Jun S. Liu, 2000. "Mixture Kalman filters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 493-508.
    4. Nicolas Chopin, 2007. "Dynamic Detection of Change Points in Long Time Series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 349-366, June.
    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. 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.

    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. 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.
    2. Karamé, Frédéric, 2018. "A new particle filtering approach to estimate stochastic volatility models with Markov-switching," Econometrics and Statistics, Elsevier, vol. 8(C), pages 204-230.
    3. 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.
    4. 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.
    5. Crisan, D. & Li, K., 2015. "Generalised particle filters with Gaussian mixtures," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2643-2673.
    6. Andreas Hetland, 2018. "The Stochastic Stationary Root Model," Econometrics, MDPI, vol. 6(3), pages 1-33, August.
    7. 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.
    8. 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.
    9. 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.
    10. Beran, Jan & Feng, Yuanhua, 1999. "Local Polynomial Estimation with a FARIMA-GARCH Error Process," CoFE Discussion Papers 99/08, University of Konstanz, Center of Finance and Econometrics (CoFE).
    11. Corbet, Shaen & Larkin, Charles & McMullan, Caroline, 2020. "The impact of industrial incidents on stock market volatility," Research in International Business and Finance, Elsevier, vol. 52(C).
    12. Cho, Guedae & Kim, MinKyoung & Koo, Won W., 2003. "Relative Agricultural Price Changes In Different Time Horizons," 2003 Annual meeting, July 27-30, Montreal, Canada 22249, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    13. Minot, Nicholas, 2014. "Food price volatility in sub-Saharan Africa: Has it really increased?," Food Policy, Elsevier, vol. 45(C), pages 45-56.
    14. Umar, Muhammad & Mirza, Nawazish & Rizvi, Syed Kumail Abbas & Furqan, Mehreen, 2023. "Asymmetric volatility structure of equity returns: Evidence from an emerging market," The Quarterly Review of Economics and Finance, Elsevier, vol. 87(C), pages 330-336.
    15. Shively, Gerald E., 2001. "Price thresholds, price volatility, and the private costs of investment in a developing country grain market," Economic Modelling, Elsevier, vol. 18(3), pages 399-414, August.
    16. Lahmiri, Salim & Bekiros, Stelios, 2017. "Disturbances and complexity in volatility time series," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 38-42.
    17. Hao Chen & Qiulan Wan & Yurong Wang, 2014. "Refined Diebold-Mariano Test Methods for the Evaluation of Wind Power Forecasting Models," Energies, MDPI, vol. 7(7), pages 1-14, July.
    18. Tomanova, Lucie, 2013. "Exchange Rate Volatility and the Foreign Trade in CEEC," EY International Congress on Economics I (EYC2013), October 24-25, 2013, Ankara, Turkey 267, Ekonomik Yaklasim Association.
    19. Chang, Chia-Lin, 2015. "Modelling a latent daily Tourism Financial Conditions Index," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 113-126.
    20. Jumah, Adusei & Kunst, Robert M., 2001. "The Effects of Exchange-Rate Exposures on Equity Asset Markets," Economics Series 94, Institute for Advanced Studies.

    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:121:y:2011:i:1:p:38-60. 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.