IDEAS home Printed from https://ideas.repec.org/p/bep/unimip/unimi-1114.html

On a family of test statistics for discretely observed diffusion processes

Author

Listed:
  • Alessandro De Gregorio

    (University of Rome, La Sapienza)

  • Stefano Iacus

    (Department of Economics, Business and Statistics, University of Milan, IT)

Abstract

We consider parametric hypotheses testing for multidimensional ergodic diffusion processes observed at discrete time. We propose a family of test statistics, related to the so called phi-divergence measures. By taking into account the quasi-likelihood approach developed for studying the stochastic differential equations, it is proved that the tests in this family are all asymptotically distribution free. In other words, our test statistics weakly converge to the chi squared distribution. Furthermore, our test statistic is compared with the quasi likelihood ratio test. In the case of contiguous alternatives, it is also possible to study in detail the power function of the tests. Although all the tests in this family are asymptotically equivalent, we show by Monte Carlo analysis that, in the small sample case, the performance of the test strictly depends on the choice of the function phi. Furthermore, in this framework, the simulations show that there are not uniformly most powerful tests.

Suggested Citation

  • Alessandro De Gregorio & Stefano Iacus, 2011. "On a family of test statistics for discretely observed diffusion processes," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1114, Universitá degli Studi di Milano.
    • Handle: RePEc:bep:unimip:unimi-1114
    Note: oai:cdlib1:unimi-1114
    as

    Download full text from publisher

    File URL: http://services.bepress.com/unimi/statistics/art53
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

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


    Cited by:

    1. Papanicolaou, Alex & Giesecke, Kay, 2016. "Variation-based tests for volatility misspecification," Journal of Econometrics, Elsevier, vol. 191(1), pages 217-230.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:bep:unimip:unimi-1114. 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: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/damilit.html .

    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.