IDEAS home Printed from
   My bibliography  Save this paper

On a family of test statistics for discretely observed diffusion processes


  • Alessandro DE GREGORIO


  • Stefano Maria IACUS



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 Maria IACUS, 2011. "On a family of test statistics for discretely observed diffusion processes," Departmental Working Papers 2011-37, Department of Economics, Management and Quantitative Methods at Universit√† degli Studi di Milano.
  • Handle: RePEc:mil:wpdepa:2011-37

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Morales, D. & Pardo, L. & Vajda, I., 1997. "Some New Statistics for Testing Hypotheses in Parametric Models, ," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 137-168, July.
    2. Giet, Ludovic & Lubrano, Michel, 2008. "A minimum Hellinger distance estimator for stochastic differential equations: An application to statistical inference for continuous time interest rate models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2945-2965, February.
    3. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

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


    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:mil:wpdepa:2011-37. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (DEMM Working Papers) The email address of this maintainer does not seem to be valid anymore. Please ask DEMM Working Papers to update the entry or send us the correct email address. General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.