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Time series segmentation: A sliding window approach. (English) Zbl 0869.62059

Summary: The aim of this paper is to present two on-line, sliding window segmentation algorithms. Detecting nonstationarity is based on parameter fluctuations and change point localization of the Akaike information criterion. Asymptotic properties of the proposed algorithms are analyzed. Specifically, the limiting distributions are derived and the asymptotic threshold values are tabulated for future reference. Finite sample simulations are performed to illustrate the usefulness of these algorithms.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P20 Applications of statistics to economics
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[1] Andrews, D., Heteroskedasticity and autocorrelation consistent covariance matrix estimation, Econometrica, 59, 817-858 (1991) · Zbl 0732.62052
[2] Andrews, D., Tests for parameter instability and structural change with unknown change points, Econometrica, 61, 821-856 (1993) · Zbl 0795.62012
[3] Andrews, D.; Ploberger, W., Optimal tests when a nuisance parameter is present only under the alternative, Econometrica (1994) · Zbl 0815.62033
[4] Appeal, U.; Brandt, A., Adaptive sequential segmentation of piecewise stationary time series, Information Sciences, 29, 27-56 (1983) · Zbl 0584.62155
[5] Bai, J., Estimation of structural change in econometric models (1991), Department of Economics, University of California: Department of Economics, University of California Berkeley, Working Paper
[6] Basseville, M.; Benveniste, A., Sequential segmentation of nonstationary digital signals using spectral analysis, Information Sciences, 29, 57-73 (1983) · Zbl 0568.94004
[7] Basseville, M.; Benveniste, A., Detection of Abrupt Changes in Signals and Dynamical Systems (1986), Springer-Verlag: Springer-Verlag New York · Zbl 0578.93056
[8] Bauer, P.; Hackl, P., The use of MOSUMS for quality control, Technometrics, 20, 431-436 (1978) · Zbl 0436.62090
[9] Billingsley, P., Convergence of Probability Measures (1968), Wiley: Wiley New York · Zbl 0172.21201
[10] Bodenstein, G.; Praetorius, H. M., Feature extraction from encephalogram by adaptive segmentation, (Proceedings IEEE, 65 (1977)), 642-652
[11] Brown, R.; Durbin, J.; Evans, J., Techniques for testing the constancy of regression relationships over time, Journal of Royal Statistical Society, B37, 149-163 (1975), Series · Zbl 0321.62063
[12] Chu, C. S.; Hornik, K.; Kuan, C. K., MOSUM test for parameter constancy (1994), University of Southern California, Working Paper
[13] Chu, C. S.; Hornik, K.; Kaun, C. M., The moving-estimates test for parameter stability, Econometric Theory (1995)
[14] Chu, C. S.; White, H., A direct test for changing trend, Journal of Business and Econometric Statistics, 10, 289-299 (1992)
[15] Cuzik, J., Boundary crossing probabilities for stationart Gaussian processes and Brownian motion, Transactions in American Mathematics Society, 263, 469-492 (1981)
[16] Deshayes, J.; Picard, D., Off-line statistical analysis of change-point problems using nonparametric and likelihood methods, (Basseville, M.; Beneniste, A., Detection of Abrupt Changes Signals and Dynamical Systems (1986), Springer-Verlag: Springer-Verlag New York) · Zbl 0534.62044
[17] Doob, J., Heuristic approach to Kologorov-Smirnov theorems, Annals of Mathematical Statistics, 20, 393-403 (1949) · Zbl 0035.08901
[18] Hawkins, D., A test for a change point in a parametric model based on a maximal Wald-type statistic, Sankhya, 49, 368-376 (1987) · Zbl 0639.62014
[19] Hinkley, D., Inference about the change point in a sequence of random variables, Biometrika, 57, 1-17 (1970) · Zbl 0198.51501
[20] Kramer, W.; Ploberger, W.; Alt, R., Testing structural change in dynamic models, Econometrica, 56, 1335-1369 (1988) · Zbl 0655.62107
[21] Nunes, L.; Kuan, C.-M.; Newbold, P., Spurious break (1993), Department of Economics, University of Illinois: Department of Economics, University of Illinois Urbana-Champaign, Working Paper
[22] Phillips, P.; Durlauf, S., Multiple time series regression with integrated process, Review of Economic Studies, 53, 473-495 (1986) · Zbl 0599.62103
[23] Ploberger, W.; Kramer, W.; Kontrus, K., A new test for structural stability in the linear regression model, Journal of Econometrics, 40, 307-318 (1989) · Zbl 0668.62045
[24] Ploberger, W.; Kramer, W., The CUSUM test with OLS residuals, Econometrica, 60, 271-285 (1992) · Zbl 0744.62155
[25] Ploberger, W.; Kramer, W.; Alt, A., Testing for structural change in dynamic models, Econometrica, 60, 271-285 (1988)
[26] Pollard, D., Convergence of Stochastic Processes (1984), Springer-Verlag: Springer-Verlag New York · Zbl 0544.60045
[27] Quandt, R., Tests of the hypothesis that a linear regression system obeying two separate regimes, Journal of the American Statistical Association, 55, 324-330 (1960) · Zbl 0095.13602
[28] Sen, P., Asymptotic theory of some tests for a possible change in the regression slope occurring at unknown time point, Zeitschrift Wahrscheinlichkeitstheorie und Verwandte Gebiete, 52, 203-218 (1980) · Zbl 0416.62066
[29] Willsky, A. S., A survey of design methods for failure detection in dynamic systems, Automatica, 12, 601-611 (1976) · Zbl 0345.93067
[30] Wooldridge, J.; White, H., Some invariance principles and central limit theorem for dependent heterogeneous processes, Econometric Theory, 4, 210-230 (1988)
[31] Zacks, S., Survey of classical and Bayesian approaches to the change point problem: Fixed sample and sequential procedures for testing and estimation, (Rivzi, M. H.; etal., Recent Advances in Statistics (1983)) · Zbl 0563.62062
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