IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v27y2006i1p77-97.html
   My bibliography  Save this article

An Approximate Innovation Method For The Estimation Of Diffusion Processes From Discrete Data

Author

Listed:
  • J. C. Jimenez
  • T. Ozaki

Abstract

. In this paper, an approximate innovation method is introduced for the estimation of diffusion processes, given a set of discrete and noisy observations of some of their components. The method is based on a recent extension of local linearization filters to the general case of continuous–discrete state–space models with multiplicative noise. This filtering method provides adequate approximations for the prediction and filter estimates that are required by the innovation method in the estimation of the unknown parameters and the unobserved component of the diffusion process. The performance of approximate innovation estimators is illustrated by means of numerical simulations.

Suggested Citation

  • J. C. Jimenez & T. Ozaki, 2006. "An Approximate Innovation Method For The Estimation Of Diffusion Processes From Discrete Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 77-97, January.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:1:p:77-97
    DOI: 10.1111/j.1467-9892.2005.00454.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2005.00454.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.2005.00454.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. T. Ozaki & J. C. Jimenez & V. Haggan‐Ozaki, 2000. "The Role of the Likelihood Function in the Estimation of Chaos Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(4), pages 363-387, July.
    2. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.
    3. Brigo, Damiano & Hanzon, Bernard, 1998. "On some filtering problems arising in mathematical finance," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 53-64, May.
    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. J. Jimenez & R. Biscay & T. Ozaki, 2005. "Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(2), pages 109-141, June.
    2. Quentin J M Huys & Liam Paninski, 2009. "Smoothing of, and Parameter Estimation from, Noisy Biophysical Recordings," PLOS Computational Biology, Public Library of Science, vol. 5(5), pages 1-16, May.
    3. Arenas, Zochil González & Jimenez, Juan Carlos & Lozada-Chang, Li-Vang & Santana, Roberto, 2021. "Estimation of distribution algorithms for the computation of innovation estimators of diffusion processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 449-467.

    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. Arenas, Zochil González & Jimenez, Juan Carlos & Lozada-Chang, Li-Vang & Santana, Roberto, 2021. "Estimation of distribution algorithms for the computation of innovation estimators of diffusion processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 449-467.
    2. J. Jimenez & R. Biscay & T. Ozaki, 2005. "Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(2), pages 109-141, June.
    3. Jury Falini, 2009. "Pricing caps with HJM models: the benefits of humped volatility," Department of Economics University of Siena 563, Department of Economics, University of Siena.
    4. Hermann Singer, 2011. "Continuous-discrete state-space modeling of panel data with nonlinear filter algorithms," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(4), pages 375-413, December.
    5. Aliu, A. Hassan & Abiodun A. A. & Ipinyomi R.A., 2017. "Statistical Inference for Discretely Observed Diffusion Epidemic Models," International Journal of Mathematics Research, Conscientia Beam, vol. 6(1), pages 29-35.
    6. Andrea Gombani & Wolfgang J. Runggaldier, 2001. "A Filtering Approach To Pricing In Multifactor Term Structure Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 303-320.
    7. Michele Bianchi & Frank Fabozzi, 2015. "Investigating the Performance of Non-Gaussian Stochastic Intensity Models in the Calibration of Credit Default Swap Spreads," Computational Economics, Springer;Society for Computational Economics, vol. 46(2), pages 243-273, August.
    8. Giuliano De Rossi, 2004. "Maximum likelihood estimation of the Cox-Ingersoll-Ross model using particle filters," Computing in Economics and Finance 2004 302, Society for Computational Economics.
    9. Baaquie, Belal E. & Pan, Tang, 2011. "Simulation of coupon bond European and barrier options in quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 263-289.
    10. Robert J. Elliott & John W. Lau & Hong Miao & Tak Kuen Siu, 2012. "Viterbi-Based Estimation for Markov Switching GARCH Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(3), pages 219-231, August.
    11. Falini, Jury, 2010. "Pricing caps with HJM models: The benefits of humped volatility," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1358-1367, December.
    12. Isao Shoji & Masahiro Nozawa, 2020. "A geometric analysis of nonlinear dynamics and its application to financial time series," Papers 2012.11825, arXiv.org.
    13. Wolfgang Lemke & Deutsche Bundesbank, 2006. "Term Structure Modeling and Estimation in a State Space Framework," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-28344-7, October.
    14. Damiano Brigo & Jan Liinev, 2005. "On the distributional distance between the lognormal LIBOR and swap market models," Quantitative Finance, Taylor & Francis Journals, vol. 5(5), pages 433-442.
    15. Damiano Brigo & Mirela Predescu & Agostino Capponi, 2010. "Credit Default Swaps Liquidity modeling: A survey," Papers 1003.0889, arXiv.org, revised Mar 2010.
    16. Aleš Černý & Jan Kallsen, 2008. "Mean–Variance Hedging And Optimal Investment In Heston'S Model With Correlation," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 473-492, July.
    17. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    18. Gonon, Lukas & Teichmann, Josef, 2020. "Linearized filtering of affine processes using stochastic Riccati equations," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 394-430.
    19. Antje Berndt & Peter Ritchken & Zhiqiang Sun, 2010. "On Correlation and Default Clustering in Credit Markets," The Review of Financial Studies, Society for Financial Studies, vol. 23(7), pages 2680-2729, July.
    20. Gombani, Andrea & Jaschke, Stefan R. & Runggaldier, Wolfgang J., 2005. "A filtered no arbitrage model for term structures from noisy data," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 381-400, March.

    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:bla:jtsera:v:27:y:2006:i:1:p:77-97. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.