IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i4p1235-1256.html
   My bibliography  Save this article

Forgetting the initial distribution for Hidden Markov Models

Author

Listed:
  • Douc, R.
  • Fort, G.
  • Moulines, E.
  • Priouret, P.

Abstract

The forgetting of the initial distribution for discrete Hidden Markov Models (HMM) is addressed: a new set of conditions is proposed, to establish the forgetting property of the filter, at a polynomial and geometric rate. Both a pathwise-type convergence of the total variation distance of the filter started from two different initial distributions, and a convergence in expectation are considered. The results are illustrated using different HMM of interest: the dynamic tobit model, the nonlinear state space model and the stochastic volatility model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:4:p:1235-1256
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(08)00104-X
    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. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    2. Moral, P. Del & Guionnet, A., 1998. "Large deviations for interacting particle systems: Applications to non-linear filtering," Stochastic Processes and their Applications, Elsevier, vol. 78(1), pages 69-95, October.
    3. Budhiraja, A. & Ocone, D., 1999. "Exponential stability in discrete-time filtering for non-ergodic signals," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 245-257, August.
    4. 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.
    5. 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.
    6. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
    7. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    8. Aurora Manrique & Neil Shephard, 1998. "Simulation-based likelihood inference for limited dependent processes," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 174-202.
    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. 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.
    2. 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.
    3. 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.
    4. 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..
    5. 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.
    6. Whiteley, Nick, 2021. "Dimension-free Wasserstein contraction of nonlinear filters," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 31-50.

    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. Pitt, Michael K., 2002. "Smooth particle filters for likelihood evaluation and maximisation," Economic Research Papers 269464, University of Warwick - Department of Economics.
    2. 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.
    3. Michael Pitt & Sheheryar Malik & Arnaud Doucet, 2014. "Simulated likelihood inference for stochastic volatility models using continuous particle filtering," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 527-552, June.
    4. Siem Jan Koopman & Eugenie Hol Uspensky, 2002. "The stochastic volatility in mean model: empirical evidence from international stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 667-689.
    5. 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.
    6. 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.
    7. Manabu Asai & Michael McAleer, 2011. "Alternative Asymmetric Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 30(5), pages 548-564, October.
    8. Daniel B. Nelson, 1994. "Asymptotically Optimal Smoothing with ARCH Models," NBER Technical Working Papers 0161, National Bureau of Economic Research, Inc.
    9. Philippe Goulet Coulombe & Mikael Frenette & Karin Klieber, 2023. "From Reactive to Proactive Volatility Modeling with Hemisphere Neural Networks," Working Papers 23-04, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management, revised Nov 2023.
    10. Robert Azencott & Yutheeka Gadhyan & Roland Glowinski, 2014. "Option Pricing Accuracy for Estimated Heston Models," Papers 1404.4014, arXiv.org, revised Jul 2015.
    11. Luc Bauwens & Michel Lubrano, 2007. "Bayesian Inference in Dynamic Disequilibrium Models: An Application to the Polish Credit Market," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 469-486.
    12. Qiang Zhang & Rui Luo & Yaodong Yang & Yuanyuan Liu, 2018. "Benchmarking Deep Sequential Models on Volatility Predictions for Financial Time Series," Papers 1811.03711, arXiv.org.
    13. Zhang, Xibin & King, Maxwell L., 2008. "Box-Cox stochastic volatility models with heavy-tails and correlated errors," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 549-566, June.
    14. Davide Raggi & Silvano Bordignon, 2011. "Volatility, Jumps, and Predictability of Returns: A Sequential Analysis," Econometric Reviews, Taylor & Francis Journals, vol. 30(6), pages 669-695.
    15. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range‐Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    16. Nelson, Daniel B. & Foster, Dean P., 1995. "Filtering and forecasting with misspecified ARCH models II : Making the right forecast with the wrong model," Journal of Econometrics, Elsevier, vol. 67(2), pages 303-335, June.
    17. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
    18. Willy Alanya & Gabriel Rodríguez, 2018. "Stochastic Volatility in the Peruvian Stock Market and Exchange Rate Returns: A Bayesian Approximation," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 17(3), pages 354-385, December.
    19. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    20. Stentoft, Lars, 2011. "American option pricing with discrete and continuous time models: An empirical comparison," Journal of Empirical Finance, Elsevier, vol. 18(5), pages 880-902.

    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:4:p:1235-1256. 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.