Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Multiple Structural Change-Point Estimation in Linear Regression Models

  • Kim, Jae-Hee (Department of Statistics, Duksung Women's University)
  • Received : 2012.02.16
  • Accepted : 2012.04.02
  • Published : 2012.05.31
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Abstract

This paper is concerned with the detection of multiple change-points in linear regression models. The proposed procedure relies on the local estimation for global change-point estimation. We propose a multiple change-point estimator based on the local least squares estimators for the regression coefficients and the split measure when the number of change-points is unknown. Its statistical properties are shown and its performance is assessed by simulations and real data applications.

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References

  1. Andrews, D. W. K. (1993). Tests for parameter instability and structural changes with unknown change point, Econometrica, 61, 821-856. https://doi.org/10.2307/2951764
  2. Andrews D. W. K. and Ploberger, W. (1994). Optimal tests when a nuisance parameter is present only under the alternative, Econometrica, 62, 1383-1414. https://doi.org/10.2307/2951753
  3. Bai, J. and Perron, P. (1998). Estimating and testing linear models with multiple structural changes, Econometrica, 66, 47-78. https://doi.org/10.2307/2998540
  4. Bai, J. and Perron, P. (2003). Computation and analysis of multiple structural change models, Journal of Applied Econometrics, 18, 1-22. https://doi.org/10.1002/jae.659
  5. Bauer, P. and Hackl, P. (1978). The use of MOSUMs for quality control, Technometrics, 20, 431-436.
  6. Broemeling, L. D. and Tsurumi, H. (1987). Econometrics and Structural Change, Dekker, New York.
  7. Brown, L. R., Durbin, J. and Evans, J. M. (1975). Techniques for testing the constancy of regression relationships over time, Journal of Royal Statistical Society B, 37, 149-192.
  8. Chu, C. J., Hornik, K. and Kuan, C. (1995). MOSUM tests for parameter constancy, Biometrika, 82, 603-617. https://doi.org/10.1093/biomet/82.3.603
  9. Chib, S. (1998). Estimation and comparison of multiple change-point models, Journal of Econometrics, 86, 221-241. https://doi.org/10.1016/S0304-4076(97)00115-2
  10. Cobb, G. W. (1978). The problem of Nile: Conditional solution to a change-point problem, Biometrika, 65, 243-251. https://doi.org/10.1093/biomet/65.2.243
  11. Dufour, J.-M. and Ghysels, E. (1996). Recent developments in the econometrics of structural change, Journal of Econometrics, 70, 1-8. https://doi.org/10.1016/0304-4076(94)01681-X
  12. Gregoire, G. and Hamrouni, Z. (2002). Change-point estimation by local linear smoothing, Journal of Multivariate Analysis, 83, 56-83. https://doi.org/10.1006/jmva.2001.2038
  13. Kim, J. and Cheon, S. (2010a). Bayesian multiple change-point estimation with annealing stochastic approximation Monte Carlo, Computational Statistics, 25, 215-239. https://doi.org/10.1007/s00180-009-0172-x
  14. Kim, J. and Cheon, S. (2010b). A Bayesian regime-switching time series model, Journal of Time Series Analysis, 31, 365-378. https://doi.org/10.1111/j.1467-9892.2010.00670.x
  15. Kim, J. and Hart, J. D. (2010). A change-point estimator using local Fourier series, Journal of Nonparametric Statistics, 23, 83-98.
  16. Koop, G. M. and Porter, S. M. (2004). Forecasting and estimating multiple change-point models with an unknown number of change-points, U of Leicester, Working paper No. 04/31.
  17. Lavielle, M. and Lebarbier, E. (2001). An application of MCMC methods for the multiple changepoints problem, Signal Processing, 81, 39-53. https://doi.org/10.1016/S0165-1684(00)00189-4
  18. Loader, C. R. (1996). Change point estimation using nonparametric regression, Annals of Statistics, 24, 1667-1678. https://doi.org/10.1214/aos/1032298290
  19. McDonald, J. A. and Owen, A. B. (1986). Smoothing with split linear fits, Technometrics, 28, 195-208. https://doi.org/10.1080/00401706.1986.10488127
  20. Perron, P. and Zhu, X. (2005). Structural breaks with deterministic and stochastic trends, Journal of Econometrics, 129, 65-119. https://doi.org/10.1016/j.jeconom.2004.09.004
  21. Ploberger, W. and Kramer, W. (1992). The cusum test with OLS residuals, Econometrica, 60, 271-285. https://doi.org/10.2307/2951597
  22. Rice, J. (1984). Bandwidth choice for nonparametric regression, Annals of statistics, 12, 1215-1230. https://doi.org/10.1214/aos/1176346788