IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v122y2013icp292-316.html
   My bibliography  Save this article

On a family of test statistics for discretely observed diffusion processes

Author

Listed:
  • De Gregorio, A.
  • Iacus, S.M.

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 ϕ-divergence measures. It is proved that the test statistics in this family are all asymptotically distribution free and converge to the chi squared distribution. In the case of contiguous alternatives, it is also possible to study in detail the power function of the tests.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:292-316
    DOI: 10.1016/j.jmva.2013.08.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13001632
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.08.002?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    2. 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.
    3. 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.
    4. 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.
    5. Yasutaka Shimizu, 2006. "M-Estimation for Discretely Observed Ergodic Diffusion Processes with Infinitely Many Jumps," Statistical Inference for Stochastic Processes, Springer, vol. 9(2), pages 179-225, July.
    6. 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.
    7. 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.
    8. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    9. T. Ogihara & N. Yoshida, 2011. "Quasi-likelihood analysis for the stochastic differential equation with jumps," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 189-229, October.
    10. De Gregorio, Alessandro & Iacus, Stefano M., 2012. "Adaptive Lasso-Type Estimation For Multivariate Diffusion Processes," Econometric Theory, Cambridge University Press, vol. 28(4), pages 838-860, August.
    Full references (including those not matched with items on IDEAS)

    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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Yasutaka Shimizu, 2017. "Threshold Estimation for Stochastic Processes with Small Noise," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 951-988, December.
    6. 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.
    7. Mitsuki Kobayashi & Yasutaka Shimizu, 2023. "Threshold estimation for jump-diffusions under small noise asymptotics," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 361-411, July.
    8. 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.
    9. 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.
    10. 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.
    11. Nakahiro Yoshida, 2022. "Quasi-likelihood analysis and its applications," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 43-60, April.
    12. 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.
    13. Jakobsen, Nina Munkholt & Sørensen, Michael, 2019. "Estimating functions for jump–diffusions," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3282-3318.
    14. 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.
    15. Yiying Cheng & Yaozhong Hu & Hongwei Long, 2020. "Generalized moment estimators for $$\alpha $$α-stable Ornstein–Uhlenbeck motions from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 53-81, April.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    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:eee:jmvana:v:122:y:2013:i:c:p:292-316. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.