IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v79y2009i4p442-449.html
   My bibliography  Save this article

Particle filtering approximations for a Gaussian-generalized inverse Gaussian model

Author

Listed:
  • Ferrante, Marco
  • Frigo, Nadia

Abstract

We consider the filtering problem for a class of discrete-time partially observable stochastic processes. Under strong conditions on the parameters involved and on the initial condition, we are able to prove that it admits a finite dimensional filter. Relaxing these assumptions, we use a Rao Blackwellization procedure to perform a Particle filtering approximation of the filtering distribution, then we prove its convergence and extend this study to a jump Markov model.

Suggested Citation

  • Ferrante, Marco & Frigo, Nadia, 2009. "Particle filtering approximations for a Gaussian-generalized inverse Gaussian model," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 442-449, February.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:4:p:442-449
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00441-0
    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. Shephard, Neil, 1994. "Local scale models : State space alternative to integrated GARCH processes," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 181-202.
    2. Genon-Catalot, Valentine, 2003. "A non-linear explicit filter," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 145-154, January.
    3. Ferrante, Marco & Vidoni, Paolo, 1999. "A Gaussian-generalized inverse Gaussian finite-dimensional filter," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 165-176, November.
    4. P. Vidoni, 1999. "Exponential family state space models based on a conjugate latent process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 213-221.
    5. Ferrante, Marco & Vidoni, Paolo, 1998. "Finite dimensional filters for nonlinear stochastic difference equations with multiplicative noises," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 69-81, September.
    Full references (including those not matched with items on IDEAS)

    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. Ferrante, Marco & Vidoni, Paolo, 1999. "A Gaussian-generalized inverse Gaussian finite-dimensional filter," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 165-176, November.
    2. de Pinho, Frank M. & Franco, Glaura C. & Silva, Ralph S., 2016. "Modeling volatility using state space models with heavy tailed distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 108-127.
    3. Vidoni Paolo, 2004. "Constructing Non-linear Gaussian Time Series by Means of a Simplified State Space Representation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-20, May.
    4. Chaleyat-Maurel, Mireille & Genon-Catalot, Valentine, 2006. "Computable infinite-dimensional filters with applications to discretized diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1447-1467, October.
    5. Kon Kam King, Guillaume & Pandolfi, Andrea & Piretto, Marco & Ruggiero, Matteo, 2024. "Approximate filtering via discrete dual processes," Stochastic Processes and their Applications, Elsevier, vol. 168(C).
    6. Kostas Triantafyllopoulos, 2009. "Inference of Dynamic Generalized Linear Models: On‐Line Computation and Appraisal," International Statistical Review, International Statistical Institute, vol. 77(3), pages 430-450, December.
    7. T. R. Santos, 2018. "A Bayesian GED-Gamma stochastic volatility model for return data: a marginal likelihood approach," Papers 1809.01489, arXiv.org.
    8. Roberto Leon-Gonzalez & Blessings Majoni, 2023. "Exact Likelihood for Inverse Gamma Stochastic Volatility Models," GRIPS Discussion Papers 23-07, National Graduate Institute for Policy Studies.
    9. Deschamps, Philippe J., 2011. "Bayesian estimation of an extended local scale stochastic volatility model," Journal of Econometrics, Elsevier, vol. 162(2), pages 369-382, June.
    10. Bakshi, Gurdip & Skoulakis, Georgios, 2010. "Do subjective expectations explain asset pricing puzzles?," Journal of Financial Economics, Elsevier, vol. 98(3), pages 462-477, December.
    11. Ferrante, Marco & Vidoni, Paolo, 1998. "Finite dimensional filters for nonlinear stochastic difference equations with multiplicative noises," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 69-81, September.
    12. Gurdip Bakshi, 2009. "Du subjectiv expectations explain asset pricing puzzles?," 2009 Meeting Papers 1234, Society for Economic Dynamics.
    13. Charles Bos & Neil Shephard, 2006. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 219-244.
    14. Jan Patrick Hartkopf, 2023. "Composite forecasting of vast-dimensional realized covariance matrices using factor state-space models," Empirical Economics, Springer, vol. 64(1), pages 393-436, January.
    15. Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Inference under Sampling from Scale Mixtures of Normals," Other publications TiSEM 10be2f67-1679-4828-bba6-7, Tilburg University, School of Economics and Management.
    16. Uhlig, H.F.H.V.S., 1996. "Bayesian Vector Autoregressions with Stochastic Volatility," Other publications TiSEM 4fd55395-6830-46a2-9d18-e, Tilburg University, School of Economics and Management.
    17. Roberto Leon-Gonzalez & Blessings Majon, 2024. "Approximate Factor Models with a Common Multiplicative Factor for Stochastic Volatility," GRIPS Discussion Papers 24-02, National Graduate Institute for Policy Studies.
    18. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
    19. Fernández, Carmen & Steel, Mark F.J., 2000. "Bayesian Regression Analysis With Scale Mixtures Of Normals," Econometric Theory, Cambridge University Press, vol. 16(1), pages 80-101, February.
    20. Alexander Tsyplakov, 2010. "Revealing the arcane: an introduction to the art of stochastic volatility models (in Russian)," Quantile, Quantile, issue 8, pages 69-122, July.

    More about this item

    Statistics

    Access and download statistics

    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:stapro:v:79:y:2009:i:4:p:442-449. 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/622892/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.