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Use Of Cumulative Sums For Detection Of Changepoints In The Rate Parameter Of A Poisson Process

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Pedro Galeano ()
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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Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws046816.

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Date of creation: Dec 2004
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Handle: RePEc:cte:wsrepe:ws046816

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  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. [Downloadable!] (restricted)
  2. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June. [Downloadable!] (restricted)
  3. Pedro Galeano & Daniel Peña & Ruey S. Tsay, 2004. "Outlier Detection In Multivariate Time Series Via Projection Pursuit," Statistics and Econometrics Working Papers ws044211, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
  5. M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2003. "Detecting Level Shifts In The Presence Of Conditional Heteroscedasticity," Statistics and Econometrics Working Papers ws036313, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
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