IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v76y2006i14p1494-1502.html
   My bibliography  Save this article

The Bickel-Rosenblatt test for diffusion processes

Author

Listed:
  • Lee, Sangyeol

Abstract

In this paper, we consider the Bickel-Rosenblatt test for a class of diffusion processes that covers the Ornstein-Uhlenbeck process. Using the discrete sampling scheme, we calculate residuals and construct the residual based Bickel-Rosenblatt test. We show that the test statistic is asymptotically normal under regularity conditions. The result is applicable to the test for the existence of jumps in diffusion models.

Suggested Citation

  • Lee, Sangyeol, 2006. "The Bickel-Rosenblatt test for diffusion processes," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1494-1502, August.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:14:p:1494-1502
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(06)00084-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sangyeol Lee & Jeongcheol Ha & Okyoung Na & Seongryong Na, 2003. "The Cusum Test for Parameter Change in Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 781-796, December.
    2. Koichi Maekawa & Sangyeol & Lee, 2004. "The Cusum Test for Parameter Change in Regression with ARCH Errors," Econometric Society 2004 Far Eastern Meetings 606, Econometric Society.
    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

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


    Cited by:

    1. Sangyeol Lee & Hiroki Masuda, 2010. "Jarque–Bera normality test for the driving Lévy process of a discretely observed univariate SDE," Statistical Inference for Stochastic Processes, Springer, vol. 13(2), pages 147-161, June.

    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. Youngmi Lee & Sangyeol Lee, 2019. "CUSUM test for general nonlinear integer-valued GARCH models: comparison study," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1033-1057, October.
    2. Okyoung Na & Jiyeon Lee & Sangyeol Lee, 2013. "Change point detection in SCOMDY models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(3), pages 215-238, July.
    3. Haejune Oh & Sangyeol Lee, 2018. "On score vector- and residual-based CUSUM tests in ARMA–GARCH models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 385-406, August.
    4. Jiwon Kang & Sangyeol Lee, 2014. "Parameter Change Test for Poisson Autoregressive Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1136-1152, December.
    5. Deng, Ai & Perron, Pierre, 2008. "The Limit Distribution Of The Cusum Of Squares Test Under General Mixing Conditions," Econometric Theory, Cambridge University Press, vol. 24(3), pages 809-822, June.
    6. Habibi Reza, 2011. "A note on approximating distribution functions of cusum and cusumsq tests," Monte Carlo Methods and Applications, De Gruyter, vol. 17(1), pages 1-10, January.
    7. Manh Cuong Dong & Cathy W. S. Chen & Sangyoel Lee & Songsak Sriboonchitta, 2019. "How Strong is the Relationship Among Gold and USD Exchange Rates? Analytics Based on Structural Change Models," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 343-366, January.
    8. Lee, Sangyeol & Park, Siyun, 2009. "The monitoring test for the stability of regression models with nonstationary regressors," Economics Letters, Elsevier, vol. 105(3), pages 250-252, December.
    9. Ai Deng & Pierre Perron, 2005. "The Limit Distribution of the CUSUM of Square Test Under Genreal MIxing Conditions," Boston University - Department of Economics - Working Papers Series WP2005-046, Boston University - Department of Economics.
    10. Haejune Oh & Sangyeol Lee, 2019. "Modified residual CUSUM test for location-scale time series models with heteroscedasticity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1059-1091, October.
    11. Badagian Baharian, Ana Laura & Kaiser Remiro, Regina & Peña, Daniel, 2013. "The change-point problem and segmentation of processes with conditional heteroskedasticity," DES - Working Papers. Statistics and Econometrics. WS ws131718, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Lu, Xinhong & Maekawa, Koichi & Lee, Sangyeol, 2008. "The CUSUM of squares test for the stability of regression models with non-stationary regressors," Economics Letters, Elsevier, vol. 100(2), pages 234-237, August.
    13. Konstantin P. Belyaev & Andrey K. Gorshenin & Victor Yu. Korolev & Anastasiia A. Osipova, 2024. "Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments," Mathematics, MDPI, vol. 12(2), pages 1-21, January.
    14. Sang Hoon Kang & Seong-Min Yoon, 2010. "Sudden Changes and Persistence in Volatility of Korean Equity Sector Returns," Korean Economic Review, Korean Economic Association, vol. 26, pages 431-451.
    15. Lajos Horvath & Lorenzo Trapani, 2021. "Changepoint detection in random coefficient autoregressive models," Papers 2104.13440, arXiv.org.
    16. Shoji, Isao, 1997. "A note on asymptotic properties of the estimator derived from the Euler method for diffusion processes at discrete times," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 153-159, December.
    17. Borzykh, Dmitriy & Yazykov, Artem, 2019. "The new KS method for a structural break detection in GARCH(1,1) models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 54, pages 90-104.
    18. Selim Amrouni & Aymeric Moulin & Tucker Balch, 2022. "CTMSTOU driven markets: simulated environment for regime-awareness in trading policies," Papers 2202.00941, arXiv.org, revised Feb 2022.
    19. Fuxiao Li & Mengli Hao & Lijuan Yang, 2021. "Structural change detection in ordinal time series," PLOS ONE, Public Library of Science, vol. 16(8), pages 1-16, August.
    20. 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.

    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:stapro:v:76:y:2006:i:14:p:1494-1502. 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.