IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/ws046816.html

Use of cumulative sums for detection of changepoints in the rate parameter of a poisson process

Author

Listed:
  • Galeano, Pedro

Abstract

This paper studies the problem of multiple changepoints in rate parameter of a Poisson process. We propose a binary segmentation algorithm in conjunction with a cumulative sums statistic for detection of changepoints such that in each step we need only to test the presence of a simple changepoint. We derive the asymptotic distribution of the proposed statistic, prove its consistency and obtain the limiting distribution of the estimate of the changepoint. A Monte Carlo analysis shows the good performance of the proposed procedure, which is illustrated with a real data example.

Suggested Citation

  • Galeano, Pedro, 2004. "Use of cumulative sums for detection of changepoints in the rate parameter of a poisson process," DES - Working Papers. Statistics and Econometrics. WS ws046816, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws046816
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/452fac19-bd35-4c90-b095-a15fefda3cea/content
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    2. Jushan Bai, 1994. "Least Squares Estimation Of A Shift In Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 453-472, September.
    3. Hawkins, Douglas M., 2001. "Fitting multiple change-point models to data," Computational Statistics & Data Analysis, Elsevier, vol. 37(3), pages 323-341, September.
    4. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
    5. Galeano, Pedro & Peña, Daniel & Tsay, Ruey S., 2004. "Outlier detection in multivariate time series via projection pursuit," DES - Working Papers. Statistics and Econometrics. WS ws044211, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Galeano, Pedro & Pena, Daniel & Tsay, Ruey S., 2006. "Outlier Detection in Multivariate Time Series by Projection Pursuit," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 654-669, June.
    7. Jandhyala, Venkata K. & Fotopoulos, Stergios B. & Evaggelopoulos, Nicholas E., 2000. "A comparison of unconditional and conditional solutions to the maximum likelihood estimation of a change-point," Computational Statistics & Data Analysis, Elsevier, vol. 34(3), pages 315-334, September.
    8. Bradley P. Carlin & Alan E. Gelfand & Adrian F. M. Smith, 1992. "Hierarchical Bayesian Analysis of Changepoint Problems," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 389-405, June.
    9. Tae Young Yang, 2004. "Bayesian binary segmentation procedure for detecting streakiness in sports," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(4), pages 627-637, November.
    10. Carnero, María Ángeles & Peña, Daniel & Ruiz Ortega, Esther, 2003. "Detecting level shifts in the presence of conditional heteroscedasticity," DES - Working Papers. Statistics and Econometrics. WS ws036313, Universidad Carlos III de Madrid. Departamento de Estadística.
    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. is not listed on IDEAS
    2. Wied, Dominik & Dehling, Herold & van Kampen, Maarten & Vogel, Daniel, 2014. "A fluctuation test for constant Spearman’s rho with nuisance-free limit distribution," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 723-736.
    3. Maravelakis, Petros E. & Castagliola, Philippe, 2009. "An EWMA chart for monitoring the process standard deviation when parameters are estimated," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2653-2664, May.
    4. Galeano, Pedro & Wied, Dominik, 2014. "Multiple break detection in the correlation structure of random variables," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 262-282.
    5. Pedro Galeano & Dominik Wied, 2017. "Dating multiple change points in the correlation matrix," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 331-352, 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. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    2. Bill Russell & Dooruj Rambaccussing, 2019. "Breaks and the statistical process of inflation: the case of estimating the ‘modern’ long-run Phillips curve," Empirical Economics, Springer, vol. 56(5), pages 1455-1475, May.
    3. Gianluca Mastrantonio & Giovanna Jona Lasinio & Alessio Pollice & Lorenzo Teodonio & Giulia Capotorti, 2022. "A Dirichlet process model for change‐point detection with multivariate bioclimatic data," Environmetrics, John Wiley & Sons, Ltd., vol. 33(1), February.
    4. Bill Russell & Dooruj Rambaccussing, 2016. "Breaks and the Statistical Process of Inflation: The Case of the ‘Modern’ Phillips Curve," Dundee Discussion Papers in Economics 294, Economic Studies, University of Dundee.
    5. Bakhodir A Ergashev, 2004. "Sequential Detection of US Business Cycle Turning Points: Performances of Shiryayev-Roberts, CUSUM and EWMA Procedures," Econometrics 0402001, University Library of Munich, Germany, revised 16 Mar 2004.
    6. Liang Jiang & Xiaohu Wang & Jun Yu, 2014. "On Bias in the Estimation of Structural Break Points," Working Papers 22-2014, Singapore Management University, School of Economics.
    7. Jiang, Liang & Wang, Xiaohu & Yu, Jun, 2018. "New distribution theory for the estimation of structural break point in mean," Journal of Econometrics, Elsevier, vol. 205(1), pages 156-176.
    8. Jong Hee Park, 2010. "Structural Change in U.S. Presidents' Use of Force," American Journal of Political Science, John Wiley & Sons, vol. 54(3), pages 766-782, July.
    9. Zeileis, Achim & Shah, Ajay & Patnaik, Ila, 2010. "Testing, monitoring, and dating structural changes in exchange rate regimes," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1696-1706, June.
    10. Boldea, Otilia & Hall, Alastair R., 2013. "Estimation and inference in unstable nonlinear least squares models," Journal of Econometrics, Elsevier, vol. 172(1), pages 158-167.
    11. Ruggieri, Eric & Antonellis, Marcus, 2016. "An exact approach to Bayesian sequential change point detection," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 71-86.
    12. Yann Guédon, 2013. "Exploring the latent segmentation space for the assessment of multiple change-point models," Computational Statistics, Springer, vol. 28(6), pages 2641-2678, December.
    13. Galeano, Pedro & Peña, Daniel & Tsay, Ruey S., 2004. "Outlier detection in multivariate time series via projection pursuit," DES - Working Papers. Statistics and Econometrics. WS ws044211, Universidad Carlos III de Madrid. Departamento de Estadística.
    14. KUROZUMI, Eiji & 黒住, 英司, 2017. "Confidence Sets for the Date of a Mean Shift at the End of a Sample," Discussion Papers 2017-06, Graduate School of Economics, Hitotsubashi University.
    15. Michael W. Robbins & Colin M. Gallagher & Robert B. Lund, 2016. "A General Regression Changepoint Test for Time Series Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 670-683, April.
    16. Seong Yeon Chang & Pierre Perron, 2016. "Inference on a Structural Break in Trend with Fractionally Integrated Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 555-574, July.
    17. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    18. Zeileis, Achim & Kleiber, Christian & Kramer, Walter & Hornik, Kurt, 2003. "Testing and dating of structural changes in practice," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 109-123, October.
    19. Ashok Chanabasangouda Patil & Shailesh Rastogi, 2020. "Multifractal Analysis of Market Efficiency across Structural Breaks: Implications for the Adaptive Market Hypothesis," JRFM, MDPI, vol. 13(10), pages 1-18, October.
    20. Simon C. Smith, 2020. "Equity premium prediction and structural breaks," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 25(3), pages 412-429, July.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cte:wsrepe:ws046816. 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: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    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.