IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v21y2009i3p321-343.html
   My bibliography  Save this article

Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process

Author

Listed:
  • Shota Gugushvili

Abstract

Given a discrete time sample X1, … Xn from a Lévy process X=(Xt)t≥0 of a finite jump activity, we study the problem of nonparametric estimation of the characteristic triplet (γ, σ2, ρ) corresponding to the process X. Based on Fourier inversion and kernel smoothing, we propose estimators of γ, σ2 and ρ and study their asymptotic behaviour. The obtained results include derivation of upper bounds on the mean square error of the estimators of γ and σ2 and an upper bound on the mean integrated square error of an estimator of ρ.

Suggested Citation

  • Shota Gugushvili, 2009. "Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(3), pages 321-343.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:3:p:321-343
    DOI: 10.1080/10485250802645824
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485250802645824
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485250802645824?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
    ---><---

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

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Johanna Kappus & Markus Reiß, 2010. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 314-328.
    2. Söhl, Jakob, 2010. "Polar sets for anisotropic Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 840-847, May.
    3. Johanna Kappus, 2012. "Nonparametric adaptive estimation of linear functionals for low frequency observed Lévy processes," SFB 649 Discussion Papers SFB649DP2012-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Kappus, Johanna, 2014. "Adaptive nonparametric estimation for Lévy processes observed at low frequency," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 730-758.
    5. Reiß, Markus, 2013. "Testing the characteristics of a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2808-2828.
    6. Johanna Kappus & Markus Reiß, 2010. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," SFB 649 Discussion Papers SFB649DP2010-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Brockwell, Peter J. & Schlemm, Eckhard, 2013. "Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 217-251.
    8. Zhang, Zhimin & Yang, Hailiang, 2014. "Nonparametric estimation for the ruin probability in a Lévy risk model under low-frequency observation," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 168-177.
    9. Richard Nickl & Markus Reiß, 2012. "A Donsker Theorem for Lévy Measures," SFB 649 Discussion Papers SFB649DP2012-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Fabienne Comte & Valentine Genon-Catalot, 2010. "Non-parametric estimation for pure jump irregularly sampled or noisy Lévy processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 290-313.
    11. Schmisser, Émeline, 2019. "Non parametric estimation of the diffusion coefficients of a diffusion with jumps," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5364-5405.
    12. Kato, Kengo & Kurisu, Daisuke, 2020. "Bootstrap confidence bands for spectral estimation of Lévy densities under high-frequency observations," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1159-1205.
    13. Mark Anthony Caruana, 2017. "Estimation of Lévy Processes via Stochastic Programming and Kalman Filtering," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1211-1225, December.
    14. Fabienne Comte & Céline Duval & Valentine Genon-Catalot, 2014. "Nonparametric density estimation in compound Poisson processes using convolution power estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(1), pages 163-183, January.

    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:taf:gnstxx:v:21:y:2009:i:3:p:321-343. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    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.