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The use of cumulative sums for detection of changepoints in the rate parameter of a Poisson Process

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  • 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.
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  • Galeano, Pedro, 2007. "The use of cumulative sums for detection of changepoints in the rate parameter of a Poisson Process," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6151-6165, August.
    • Handle: RePEc:eee:csdana:v:51:y:2007:i:12:p:6151-6165
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    1. 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.
    2. Hawkins, Douglas M., 2001. "Fitting multiple change-point models to data," Computational Statistics & Data Analysis, Elsevier, vol. 37(3), pages 323-341, September.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
    10. 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.
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    Cited by:

    1. 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.
    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.

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