IDEAS home Printed from https://ideas.repec.org/p/mil/wpdepa/2009-48.html
   My bibliography  Save this paper

Pseudo phi-divergence test statistics and multidimensional Ito processes

Author

Listed:
  • Alessandro DE GREGORIO
  • Stefano Maria IACUS

Abstract

We consider parametric hypotheses testing for multidimensional It\^o processes, possibly with jumps, observed at discrete time. To this aim, we propose the whole class of pseudo phi-divergence test statistics, which include as a special case the well-known likelihood ratio test but also many other test statistics as well as new ones. Although the final goal is to apply these test procedures to multidimensional Ito processes, we formulate the problem in the very general setting of regular statistical experiments and then particularize the results to our model of interest. In this general framework we prove that, contrary to what happens to true phi-divergence test statistics, the limiting distribution of the pseudo phi-divergence test statistic is characterized by the function phi which defines the divergence itself. In the case of contiguous alternatives, it is also possible to study in detail the power function of the test. Although all tests in this class are asymptotically equivalent, we show by Monte Carlo analysis that, in small sample case, the performance of the test strictly depends on the choice of the function phi. In particular, we see that even in the i. i. d. case, the power function of the generalized likelihood ratio test (phi=log) is strictly dominated by other pseudo phi-divergences test statistics.

Suggested Citation

  • Alessandro DE GREGORIO & Stefano Maria IACUS, 2009. "Pseudo phi-divergence test statistics and multidimensional Ito processes," Departmental Working Papers 2009-48, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    • Handle: RePEc:mil:wpdepa:2009-48
    as

    Download full text from publisher

    File URL: http://wp.demm.unimi.it/files/wp/2009/DEMM-2009_048wp.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Masayuki Uchida & Nakahiro Yoshida, 2004. "Information Criteria for Small Diffusions via the Theory of Malliavin–Watanabe," Statistical Inference for Stochastic Processes, Springer, vol. 7(1), pages 35-67, March.
    4. Yasutaka Shimizu & Nakahiro Yoshida, 2006. "Estimation of Parameters for Diffusion Processes with Jumps from Discrete Observations," Statistical Inference for Stochastic Processes, Springer, vol. 9(3), pages 227-277, October.
    5. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    6. S. Ajay Chandra & Masanobu Taniguchi, 2006. "Minimum α‐divergence estimation for arch models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 19-39, January.
    7. Alessandro De Gregorio & Stefano Iacus, 2008. "Divergences Test Statistics for Discretely Observed Diffusion Processes," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1076, Universitá degli Studi di Milano.
    Full references (including those not matched with items on IDEAS)

    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. De Gregorio, A. & Iacus, S.M., 2013. "On a family of test statistics for discretely observed diffusion processes," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 292-316.
    2. 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 Università degli Studi di Milano.
    3. Long, Hongwei & Ma, Chunhua & Shimizu, Yasutaka, 2017. "Least squares estimators for stochastic differential equations driven by small Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1475-1495.
    4. Chiara Amorino & Arnaud Gloter, 2020. "Contrast function estimation for the drift parameter of ergodic jump diffusion process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 279-346, June.
    5. Haruhiko Inatsugu & Nakahiro Yoshida, 2021. "Global jump filters and quasi-likelihood analysis for volatility," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 555-598, June.
    6. Nakahiro Yoshida, 2022. "Quasi-likelihood analysis and its applications," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 43-60, April.
    7. Masahiro Kurisaki, 2023. "Parameter estimation for ergodic linear SDEs from partial and discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 279-330, July.
    8. Long, Hongwei & Shimizu, Yasutaka & Sun, Wei, 2013. "Least squares estimators for discretely observed stochastic processes driven by small Lévy noises," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 422-439.
    9. Ogihara, Teppei & Yoshida, Nakahiro, 2014. "Quasi-likelihood analysis for nonsynchronously observed diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2954-3008.
    10. Alessandro Gregorio & Francesco Iafrate, 2021. "Regularized bridge-type estimation with multiple penalties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 921-951, October.
    11. Uchida, Masayuki, 2008. "Approximate martingale estimating functions for stochastic differential equations with small noises," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1706-1721, September.
    12. A. Gregorio & S. M. Iacus, 2019. "Empirical $$L^2$$ L 2 -distance test statistics for ergodic diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 233-261, July.
    13. Gloter, Arnaud & Sørensen, Michael, 2009. "Estimation for stochastic differential equations with a small diffusion coefficient," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 679-699, March.
    14. Uchida, Masayuki & Yoshida, Nakahiro, 2013. "Quasi likelihood analysis of volatility and nondegeneracy of statistical random field," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2851-2876.
    15. Yoshida, Nakahiro, 2013. "Martingale expansion in mixed normal limit," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 887-933.
    16. Masayuki Uchida, 2010. "Contrast-based information criterion for ergodic diffusion processes from discrete observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(1), pages 161-187, February.
    17. Long, Hongwei, 2009. "Least squares estimator for discretely observed Ornstein-Uhlenbeck processes with small Lévy noises," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2076-2085, October.
    18. Chiara Amorino & Arnaud Gloter, 2021. "Joint estimation for volatility and drift parameters of ergodic jump diffusion processes via contrast function," Statistical Inference for Stochastic Processes, Springer, vol. 24(1), pages 61-148, April.
    19. Yusuke Kaino & Masayuki Uchida, 2018. "Hybrid estimators for stochastic differential equations from reduced data," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 435-454, July.
    20. Masayuki Uchida & Nakahiro Yoshida, 2014. "Adaptive Bayes type estimators of ergodic diffusion processes from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 17(2), pages 181-219, July.

    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:mil:wpdepa:2009-48. 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: DEMM Working Papers (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.