IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v24y2012i4p857-882.html
   My bibliography  Save this article

Nonparametric multivariate breakpoint detection for the means, variances, and covariances of a discrete time stochastic process

Author

Listed:
  • Vincent Guigues

Abstract

We introduce a nonparametric breakpoint detection method for the means and covariances of a multivariate discrete time stochastic process. Breakpoints are defined as left or right endpoints of maximal intervals of local time homogeneity for the means and covariances. The breakpoint detection method is an adaptive algorithm that estimates the last maximal interval of homogeneity. Applied recursively, it allows us to find an arbitrary number of breakpoints. We then study a second breakpoint detection algorithm that makes use of a sliding window. The quality of both methods is analysed. For the adaptive algorithm, we provide the quality of the estimation of the one-step-ahead means and covariance matrix as well as upper bounds on the type I and type II errors when applying the procedure to a change-point model. Regarding the second method, the probability of correctly detecting the breakpoint of a change-point model is bounded from below. Numerical simulations assess the performance of both methods using simulated data.

Suggested Citation

  • Vincent Guigues, 2012. "Nonparametric multivariate breakpoint detection for the means, variances, and covariances of a discrete time stochastic process," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 857-882, December.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:857-882
    DOI: 10.1080/10485252.2012.709246
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485252.2012.709246
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485252.2012.709246?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. Spokoiny, Vladimir G., 1998. "Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice," SFB 373 Discussion Papers 1998,1, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Guigues Vincent, 2008. "Mean and covariance matrix adaptive estimation for a weakly stationary process. Application in stochastic optimization," Statistics & Risk Modeling, De Gruyter, vol. 26(2), pages 109-143, March.
    3. Fridlyand, Jane & Snijders, Antoine M. & Pinkel, Dan & Albertson, Donna G. & Jain, A.N.Ajay N., 2004. "Hidden Markov models approach to the analysis of array CGH data," Journal of Multivariate Analysis, Elsevier, vol. 90(1), pages 132-153, July.
    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. Casini, Alessandro & Perron, Pierre, 2024. "Change-point analysis of time series with evolutionary spectra," Journal of Econometrics, Elsevier, vol. 242(2).
    2. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    3. Love Michael I. & Myšičková Alena & Sun Ruping & Kalscheuer Vera & Vingron Martin & Haas Stefan A., 2011. "Modeling Read Counts for CNV Detection in Exome Sequencing Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-30, November.
    4. Denis Belomestny & Vladimir Spokoiny, 2006. "Spatial aggregation of local likelihood estimates with applications to classification," SFB 649 Discussion Papers SFB649DP2006-036, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Salvatore Fasola & Vito M. R. Muggeo & Helmut Küchenhoff, 2018. "A heuristic, iterative algorithm for change-point detection in abrupt change models," Computational Statistics, Springer, vol. 33(2), pages 997-1015, June.
    6. Härdle, Wolfgang Karl & Hautsch, Nikolaus & Mihoci, Andrija, 2012. "Local adaptive multiplicative error models for high-frequency forecasts," SFB 649 Discussion Papers 2012-031, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Huixia Judy Wang & Jianhua Hu, 2011. "Identification of Differential Aberrations in Multiple-Sample Array CGH Studies," Biometrics, The International Biometric Society, vol. 67(2), pages 353-362, June.
    8. Gao, Jiti & Gijbels, Irene & Van Bellegem, Sebastien, 2008. "Nonparametric simultaneous testing for structural breaks," Journal of Econometrics, Elsevier, vol. 143(1), pages 123-142, March.
    9. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    10. Rameen Beroukhim & Ming Lin & Yuhyun Park & Ke Hao & Xiaojun Zhao & Levi A Garraway & Edward A Fox & Ephraim P Hochberg & Ingo K Mellinghoff & Matthias D Hofer & Aurelien Descazeaud & Mark A Rubin & M, 2006. "Inferring Loss-of-Heterozygosity from Unpaired Tumors Using High-Density Oligonucleotide SNP Arrays," PLOS Computational Biology, Public Library of Science, vol. 2(5), pages 1-10, May.
    11. A. Gandolfi & M. Benelli & A. Magi & S. Chiti, 2013. "Moment estimation in discrete shifting level model applied to fast array-CGH segmentation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(3), pages 227-262, August.
    12. Yoo-Ah Kim & Stefan Wuchty & Teresa M Przytycka, 2011. "Identifying Causal Genes and Dysregulated Pathways in Complex Diseases," PLOS Computational Biology, Public Library of Science, vol. 7(3), pages 1-13, March.
    13. Bruno Spilak & Wolfgang Karl Härdle, 2022. "Tail-Risk Protection: Machine Learning Meets Modern Econometrics," Springer Books, in: Cheng-Few Lee & Alice C. Lee (ed.), Encyclopedia of Finance, edition 0, chapter 92, pages 2177-2211, Springer.
    14. Härdle, Wolfgang Karl & Mihoci, Andrija & Ting, Christopher Hian-Ann, 2014. "Adaptive order flow forecasting with multiplicative error models," SFB 649 Discussion Papers 2014-035, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Xiu Xu & Andrija Mihoci & Wolfgang Karl Hardle, 2020. "lCARE -- localizing Conditional AutoRegressive Expectiles," Papers 2009.13215, arXiv.org.
    16. Irène Gijbels & Alexandre Lambert & Peihua Qiu, 2007. "Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 235-272, June.
    17. Xu, Xiu & Mihoci, Andrija & Härdle, Wolfgang Karl, 2018. "lCARE - localizing conditional autoregressive expectiles," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 198-220.
    18. Xu, Xiu & Mihoci, Andrija & Härdle, Wolfgang Karl, 2015. "lCARE: Localizing conditional autoregressive expectiles," SFB 649 Discussion Papers 2015-052, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    19. Wolfgang Karl Härdle & Andrija Mihoci & Christopher Hian-Ann Ting, 2014. "Adaptive Order Flow Forecasting with Multiplicative Error Models," SFB 649 Discussion Papers SFB649DP2014-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    20. Fengler, Matthias & Okhrin, Ostap, 2012. "Realized Copula," Economics Working Paper Series 1214, University of St. Gallen, School of Economics and Political Science.

    More about this item

    Statistics

    Access and download statistics

    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:taf:gnstxx:v:24:y:2012:i:4:p:857-882. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    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.