IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v26y2017i2d10.1007_s10260-016-0366-7.html
   My bibliography  Save this article

Z-process method for change point problems with applications to discretely observed diffusion processes

Author

Listed:
  • Ilia Negri

    (University of Bergamo)

  • Yoichi Nishiyama

    (Waseda University)

Abstract

The aim of this paper is to develop a general, unified approach, based on some partial estimation functions which we call “Z-process”, to some change point problems in mathematical statistics. The method proposed can be applied not only to ergodic models but also to some models where the Fisher information matrix is random. Applications to some concrete models, including a parametric model for volatilities of diffusion processes are presented. Simulations for randomly time-transformed Brownian bridge process appearing as the limit of the proposed test statistics are performed with computer intensive use.

Suggested Citation

  • Ilia Negri & Yoichi Nishiyama, 2017. "Z-process method for change point problems with applications to discretely observed diffusion processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(2), pages 231-250, June.
    • Handle: RePEc:spr:stmapp:v:26:y:2017:i:2:d:10.1007_s10260-016-0366-7
    DOI: 10.1007/s10260-016-0366-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-016-0366-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-016-0366-7?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Ilia Negri & Yoichi Nishiyama, 2012. "Asymptotically distribution free test for parameter change in a diffusion process model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 911-918, October.
    2. 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.
    3. Junmo Song & Sangyeol Lee, 2009. "Test for parameter change in discretely observed diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 12(2), pages 165-183, June.
    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. Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2023. "Estimation for change point of discretely observed ergodic diffusion processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 142-183, March.
    2. Tonaki, Yozo & Uchida, Masayuki, 2023. "Change point inference in ergodic diffusion processes based on high frequency data," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 1-39.
    3. Kang, Jiwon & Song, Junmo, 2017. "Score test for parameter change in Poisson autoregressive models," Economics Letters, Elsevier, vol. 160(C), pages 33-37.
    4. Song, Junmo & Baek, Changryong, 2019. "Detecting structural breaks in realized volatility," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 58-75.
    5. Song, Junmo & Kang, Jiwon, 2018. "Parameter change tests for ARMA–GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 41-56.
    6. Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2022. "Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 397-430, July.

    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. Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2022. "Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 397-430, July.
    2. Stefano Maria IACUS & Nakahiro YOSHIDA, 2009. "Estimation for the change point of the volatility in a stochastic differential equation," Departmental Working Papers 2009-49, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    3. Koji Tsukuda, 2017. "A change detection procedure for an ergodic diffusion process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 833-864, August.
    4. Iacus, Stefano M. & Yoshida, Nakahiro, 2012. "Estimation for the change point of volatility in a stochastic differential equation," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1068-1092.
    5. Stefano M. Iacus & Nakahiro Yoshida, 2010. "Numerical Analysis of Volatility Change Point Estimators for Discretely Sampled Stochastic Differential Equations," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 39(1‐2), pages 107-127, February.
    6. Lajos Horvath & Lorenzo Trapani, 2021. "Changepoint detection in random coefficient autoregressive models," Papers 2104.13440, arXiv.org.
    7. 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.
    8. 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.
    9. Maekawa, Koichi & Lee, Sangyeol & Morimoto, Takayuki & Kawai, Ken-ichi, 2008. "Jump diffusion model with application to the Japanese stock market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(2), pages 223-236.
    10. Junmo Song & Sangyeol Lee, 2009. "Test for parameter change in discretely observed diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 12(2), pages 165-183, June.
    11. Jirak, Moritz, 2012. "Change-point analysis in increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 136-159.
    12. 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.
    13. Maria Mohr & Natalie Neumeyer, 2021. "Nonparametric volatility change detection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 529-548, June.
    14. Sangyeol Lee & Okyoung Na, 2005. "Test for parameter change based on the estimator minimizing density-based divergence measures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 553-573, September.
    15. Mamadou Lamine Diop & William Kengne, 2023. "A general procedure for change-point detection in multivariate time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 1-33, March.
    16. Vanessa Berenguer-Rico & Bent Nielsen, 2015. "Cumulated sum of squares statistics for non-linear and non-stationary regressions," Economics Papers 2015-W09, Economics Group, Nuffield College, University of Oxford.
    17. Philip Preuss & Ruprecht Puchstein & Holger Dette, 2015. "Detection of Multiple Structural Breaks in Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 654-668, June.
    18. Rafajlowicz, Ewaryst & Pawlak, Mirosław & Steland, Ansgar, 2004. "Non-parametric vertical box control chart for monitoring the mean," Technical Reports 2004,52, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    19. 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.
    20. Lee, Sangyeol, 2013. "A maximum entropy type test of fit: Composite hypothesis case," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 59-67.

    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:spr:stmapp:v:26:y:2017:i:2:d:10.1007_s10260-016-0366-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.