IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v490y2018icp439-450.html
   My bibliography  Save this article

Variance change point detection for fractional Brownian motion based on the likelihood ratio test

Author

Listed:
  • Kucharczyk, Daniel
  • Wyłomańska, Agnieszka
  • Sikora, Grzegorz

Abstract

Fractional Brownian motion is one of the main stochastic processes used for describing the long-range dependence phenomenon for self-similar processes. It appears that for many real time series, characteristics of the data change significantly over time. Such behaviour one can observe in many applications, including physical and biological experiments. In this paper, we present a new technique for the critical change point detection for cases where the data under consideration are driven by fractional Brownian motion with a time-changed diffusion coefficient. The proposed methodology is based on the likelihood ratio approach and represents an extension of a similar methodology used for Brownian motion, the process with independent increments. Here, we also propose a statistical test for testing the significance of the estimated critical point. In addition to that, an extensive simulation study is provided to test the performance of the proposed method.

Suggested Citation

  • Kucharczyk, Daniel & Wyłomańska, Agnieszka & Sikora, Grzegorz, 2018. "Variance change point detection for fractional Brownian motion based on the likelihood ratio test," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 439-450.
    • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:439-450
    DOI: 10.1016/j.physa.2017.08.134
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117308695
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2017.08.134?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. B. Tóth & F. Lillo & J. D. Farmer, 2010. "Segmentation algorithm for non-stationary compound Poisson processes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 78(2), pages 235-243, November.
    2. Inclan, Carla, 1993. "Detection of Multiple Changes of Variance Using Posterior Odds," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 289-300, July.
    3. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    4. D. A. Hsu, 1977. "Tests for Variance Shift at an Unknown Time Point," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(3), pages 279-284, November.
    5. Fryzlewicz, Piotr, 2014. "Wild binary segmentation for multiple change-point detection," LSE Research Online Documents on Economics 57146, London School of Economics and Political Science, LSE Library.
    6. Vadim Teverovsky & Murad Taqqu, 1997. "Testing for long‐range dependence in the presence of shifting means or a slowly declining trend, using a variance‐type estimator," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(3), pages 279-304, 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. Cai, Chunhao & Cheng, Xuwen & Xiao, Weilin & Wu, Xiang, 2019. "Parameter identification for mixed fractional Brownian motions with the drift parameter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    2. Muhammad Rizwan Khan & Biswajit Sarkar, 2019. "Change Point Detection for Airborne Particulate Matter ( PM 2.5 , PM 10 ) by Using the Bayesian Approach," Mathematics, MDPI, vol. 7(5), pages 1-42, May.
    3. Sikora, Grzegorz & Wyłomańska, Agnieszka & Krapf, Diego, 2018. "Recurrence statistics for anomalous diffusion regime change detection," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 380-394.
    4. Wang, Li-Na & Wang, Kai & Shen, Jiang-Long, 2020. "Weighted complex networks in urban public transportation: Modeling and testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

    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. Stefan Albert & Michael Messer & Julia Schiemann & Jochen Roeper & Gaby Schneider, 2017. "Multi-Scale Detection of Variance Changes in Renewal Processes in the Presence of Rate Change Points," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 1028-1052, November.
    2. Michael Messer, 2022. "Bivariate change point detection: Joint detection of changes in expectation and variance," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 886-916, June.
    3. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    4. Chevillon, Guillaume & Mavroeidis, Sophocles, 2011. "Learning generates Long Memory," ESSEC Working Papers WP1113, ESSEC Research Center, ESSEC Business School.
    5. Thomas Mikosch, 2004. "Is it really long memory we see in financial returns?," Econometrics 0412002, University Library of Munich, Germany.
    6. repec:ipg:wpaper:2014-078 is not listed on IDEAS
    7. Imen Zgueb Rejichi & Chaker Aloui & Duc Khuong Nguyen, 2014. "Assessing the efficiency of the MENA emerging stock markets: A sectoral perspective," Working Papers 2014-78, Department of Research, Ipag Business School.
    8. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    9. Long Hai Vo & Duc Hong Vo, 2020. "Modelling Australian Dollar Volatility at Multiple Horizons with High-Frequency Data," Risks, MDPI, vol. 8(3), pages 1-16, August.
    10. Long Hai Vo & Duc Hong Vo, 2019. "Application of Wavelet-Based Maximum Likelihood Estimator in Measuring Market Risk for Fossil Fuel," Sustainability, MDPI, vol. 11(10), pages 1-19, May.
    11. repec:ebl:ecbull:v:7:y:2007:i:1:p:1-11 is not listed on IDEAS
    12. Kim, Tae-Hwan & Leybourne, Stephen & Newbold, Paul, 2002. "Unit root tests with a break in innovation variance," Journal of Econometrics, Elsevier, vol. 109(2), pages 365-387, August.
    13. Chih-Chiang Hsu, 2000. "Long Memory or Structural Change: Testing Method and Empirical Examination," Econometric Society World Congress 2000 Contributed Papers 0867, Econometric Society.
    14. Cook, Steven, 2006. "Testing for cointegration in the presence of mis-specified structural change," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1380-1384, July.
    15. İşcanoğlu-Çekiç, Ayşegül & Gülteki̇n, Havva, 2019. "Are cross-correlations between Turkish Stock Exchange and three major country indices multifractal or monofractal?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 978-990.
    16. Demiralay, Sercan & Ulusoy, Veysel, 2014. "Value-at-risk Predictions of Precious Metals with Long Memory Volatility Models," MPRA Paper 53229, University Library of Munich, Germany.
    17. Koop, Gary & Ley, Eduardo & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian analysis of long memory and persistence using ARFIMA models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 149-169.
    18. Ngene, Geoffrey & Tah, Kenneth A. & Darrat, Ali F., 2017. "Long memory or structural breaks: Some evidence for African stock markets," Review of Financial Economics, Elsevier, vol. 34(C), pages 61-73.
    19. Anders Johansson, 2009. "An analysis of dynamic risk in the Greater China equity markets," Journal of Chinese Economic and Business Studies, Taylor & Francis Journals, vol. 7(3), pages 299-320.
    20. Zhang, Wei-Guo & Li, Zhe & Liu, Yong-Jun, 2018. "Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 402-418.
    21. Cornelis A. Los, 2004. "Nonparametric Efficiency Testing of Asian Stock Markets Using Weekly Data," Finance 0409033, University Library of Munich, Germany.
    22. Zeinali, Narges & Pourdarvish, Ahmad, 2022. "An entropy-based estimator of the Hurst exponent in fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).

    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:phsmap:v:490:y:2018:i:c:p:439-450. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.