Use of cumulative sums for detection of changepoints in the rate parameter of a poisson process
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.
|Date of creation:||Dec 2004|
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- M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2004.
"Detecting Level Shifts In The Presence Of Conditional Heteroscedasticity,"
Working Papers. Serie AD
2004-06, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Ruiz, Esther & Peña, Daniel & Carnero, María Ángeles, 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.
- Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
- Tsay, Ruey S. & Peña, Daniel & Galeano, Pedro, 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.
- 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.
- 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.
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