IDEAS home Printed from https://ideas.repec.org/p/aah/create/2012-40.html
   My bibliography  Save this paper

Limit theorems for non-degenerate U-statistics of continuous semimartingales

Author

Listed:
  • Mark Podolskij

    (Heidelberg University and CREATES)

  • Christian Schmidt

    (Heidelberg University)

  • Johanna Fasciati Ziegel

    (University of Bern)

Abstract

This paper presents the asymptotic theory for non-degenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.

Suggested Citation

  • Mark Podolskij & Christian Schmidt & Johanna Fasciati Ziegel, 2012. "Limit theorems for non-degenerate U-statistics of continuous semimartingales," CREATES Research Papers 2012-40, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2012-40
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/creates/rp/12/rp12_40.pdf
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    High frequency data; Limit theorems; Semimartingales; Stable convergence; U-statistics;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:aah:create:2012-40. 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: the person in charge (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

    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.