Least-squares estimation of an unknown number of shifts in a time series

Journal of Time Series Analysis

Volumn 21, Issue 1, 2000, Pages 33-59

  Lavielle, Marc ^a   Moulines, Eric ^b  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b TELECOM PARISTECH   (France)

Author keywords

Detection of change points; Fractional Brownian motion; H jek R nyi inequality; Penalized least squares estimate; Strongly dependent processes; Strongly mixing processes

Indexed keywords

EID: 0003074375     PISSN: 01439782     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9892.00172     Document Type: Article

References (23)

1. BAI, J., (1994), Least Square estimation of a shift in linear processes. J. Time Series Analysis, 15, 5, 453-472.
2. BAI, J. and Perron, P., (1996), Estimating and testing linear models with multiple structural changes. To appear in Econometrica.
3. BASSEVILLE, M. and NIKIFOROV, N., (1993), The Detection of abrupt changes - Theory and applications. Prentice-Hall: Information and System sciences series.
4. BATTACHARYA, P., (1987), Maximum likelihood estimation of a change-point in the distribution of independent random variables: general multiparameter case. J. of Multivariate Anal., 32, 183-208.
5. BERAN, J., (1992), Statistical methods for data with long-range dependence. Statistical Science, 7, 404-427.
6. BIRNAUM, Z. and MARSHALL, A., (1961), Some multivariate Chebyshev inequalities with extensions to continuous parameter processes. Ann. Math. Stat., 32, 682-703.
7. BRODKSY, B. and DARKHOVSKY, B., (1993), Nonparametric methods in change-point problems. Kluwer Academic Publishers, the Netherlands.
8. DOUKHAN, P., (1994), Mixing, properties and examples. Lecture notes in statistics, 85, Springer Verlag.
9. DOUKHANT, P. and LOUICHI, S., (1997), Weak dependence and moment inequalities. Preprint University Paris-Sud.
10. HÁJEK, J. and RÉNYI, A., (1955), Generalizations of an inequality of Kolmogorov. Acta. Math. Acad. Sci., 6, 281-283.
11. Ho, H. C. and HSING, T., (1997) Limit theorem for functional of moving averages, The Annals of Probability 25(4), 1636-1669.
12. HAWKINS, D., (1977), Testing a sequence of observations for a shift in location. J. Am. Statist. Assoc., 72, 180-186.
13. HINKLEY, D., (1970), Inference about the change point in a sequence of random variables. Biometrika, 57, 1-17.
14. KIM, J. and POLLARD, D., (1990), Cube root asymptotics. The Annals of Stat., 18, 191-219.
15. LIU, J., Wu, S. and ZIDEK, J., (1997), On segmented multivariate regression. Statistica Sinica, 7, 497-525.
16. MCLEISH, D., (1975), A maximal inequality and dependent strong laws. The Annals of Probability, 5, 829-839.
17. MRICZ, F., SERFLING, R. and STOUT, W., (1982), Moment and probability bounds with quasisuperadditive structure for the maximum partial sum. The Annals of Prob., 10, 4, 1032-1040.
18. PICARD, D., (1985), Testing and estimating change points in time series. J. Applied Prob., 17, 841-867.
19. Rio, E., (1995), The functional law of iterated logarithm for strongly mixing processes. The Annals of Prob., 23, 3, 1188-1203.
20. SEN, A. and SRIVASTAVA, M., (1975), On tests for detecting change in the mean. The Annals of Stat., 3, 96-103.
21. TAQQU, M., (1975), Weak convergence to the fractional Brownian motion and to the Roseblatt process. Z. Wahrsch. verw. Geb., 31, 287-302.
22. TAQQU, M., (1977), Law of the iterated logarithm for sum of non-linear functions of Gaussian variables than exhibit long range dependence. Z. Wahrsch, verw. Geb., 40, 203-238.
23. YAO, Y., (1988), Estimating the number of change-points via Schwarz criterion. Stat. & Probab. Lett., 6, 181-189.