IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v118y2008i4p649-680.html
   My bibliography  Save this article

Asymptotic properties of particle filter-based maximum likelihood estimators for state space models

Author

Listed:
  • Olsson, Jimmy
  • Rydén, Tobias

Abstract

We study the asymptotic performance of approximate maximum likelihood estimators for state space models obtained via sequential Monte Carlo methods. The state space of the latent Markov chain and the parameter space are assumed to be compact. The approximate estimates are computed by, firstly, running possibly dependent particle filters on a fixed grid in the parameter space, yielding a pointwise approximation of the log-likelihood function. Secondly, extensions of this approximation to the whole parameter space are formed by means of piecewise constant functions or B-spline interpolation, and approximate maximum likelihood estimates are obtained through maximization of the resulting functions. In this setting we formulate criteria for how to increase the number of particles and the resolution of the grid in order to produce estimates that are consistent and asymptotically normal.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:4:p:649-680
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(07)00084-1
    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. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    2. Olivier Cappé & Randal Douc & Eric Moulines & Christian Robert, 2002. "On the Convergence of the Monte Carlo Maximum Likelihood Method for Latent Variable Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(4), pages 615-635, December.
    3. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, 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. 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. Kristensen, Dennis & Salanié, Bernard, 2017. "Higher-order properties of approximate estimators," Journal of Econometrics, Elsevier, vol. 198(2), pages 189-208.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.

    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. Ahmed Bel Hadj Ayed & Gr'egoire Loeper & Fr'ed'eric Abergel, 2015. "Forecasting trends with asset prices," Papers 1504.03934, arXiv.org, revised Apr 2015.
    2. Ahmed Belhadjayed & Grégoire Loeper & Frédéric Abergel, 2016. "Forecasting Trends With Asset Prices," Post-Print hal-01512431, HAL.
    3. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
    4. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    5. María Luz Gámiz & Nikolaos Limnios & Mari Carmen Segovia-García, 2023. "The continuous-time hidden Markov model based on discretization. Properties of estimators and applications," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 525-550, October.
    6. Du, Xiaodong & Yu, Cindy L. & Hayes, Dermot J., 2011. "Speculation and volatility spillover in the crude oil and agricultural commodity markets: A Bayesian analysis," Energy Economics, Elsevier, vol. 33(3), pages 497-503, May.
    7. Kenichiro McAlinn & Asahi Ushio & Teruo Nakatsuma, 2016. "Volatility Forecasts Using Nonlinear Leverage Effects," Papers 1605.06482, arXiv.org, revised Dec 2017.
    8. Antonello Loddo & Shawn Ni & Dongchu Sun, 2011. "Selection of Multivariate Stochastic Volatility Models via Bayesian Stochastic Search," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 342-355, July.
    9. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2020. "On an integer-valued stochastic intensity model for time series of counts," MPRA Paper 105406, University Library of Munich, Germany.
    10. Maciej Kostrzewski & Jadwiga Kostrzewska, 2021. "The Impact of Forecasting Jumps on Forecasting Electricity Prices," Energies, MDPI, vol. 14(2), pages 1-17, January.
    11. Beum-Jo Park, 2011. "Forecasting Volatility in Financial Markets Using a Bivariate Stochastic Volatility Model with Surprising Information," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 37-58, September.
    12. Manabu Asai & Michael McAleer, 2011. "Alternative Asymmetric Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 30(5), pages 548-564, October.
    13. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2016. "Common Drifting Volatility in Large Bayesian VARs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 375-390, July.
    14. Genon-Catalot, Valentine, 2003. "A non-linear explicit filter," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 145-154, January.
    15. Jörn Dannemann & Hajo Holzmann, 2008. "Likelihood Ratio Testing for Hidden Markov Models Under Non‐standard Conditions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 309-321, June.
    16. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
    17. Davide Pettenuzzo & Rossen Valkanov & Allan Timmermann, 2014. "A Bayesian MIDAS Approach to Modeling First and Second Moment Dynamics," Working Papers 76, Brandeis University, Department of Economics and International Business School.
    18. Shiyi Chen & Wolfgang K. Härdle & Kiho Jeong, 2010. "Forecasting volatility with support vector machine-based GARCH model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(4), pages 406-433.
    19. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    20. Massimo Guidolin, 2013. "Markov switching models in asset pricing research," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 1, pages 3-44, Edward Elgar Publishing.

    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:118:y:2008:i:4:p:649-680. 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.