Multiscale detection and location of multiple variance changes in the presence of long memory

Journal of Statistical Computation and Simulation

Volumn 68, Issue 1, 2000, Pages 65-87

  Whitcher, Brandon ^a   Guttorp, Peter ^b   Percival, Donald B ^b  

^a EURANDOM   (Netherlands)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Cumulative sum of squares; Discrete wavelet transform; Homogeneity of variance; Maximal overlap discrete wavelet transform; Vertical ocean shear

Indexed keywords

EID: 0034348267     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949650008812056     Document Type: Article

References (23)

1. Beran, J. (1994) Statistics for Long-Memory Processes, Volume 61 of Monographs on Statistics and Applied Probability. New York: Chapman and Hall.
2. Brown, R. L., Durbin, J. and Evans, J. M. (1975) Techniques for testing the constancy of regression relationships over time. Journal of the Royal Statistical Society B, 37, 149-163.
3. Chen, J. and Gupta, A. K. (1997) Testing and locating variance changepoints with application to stock prices. Journal of the American Statistical Association, 92(438), 739-747.
4. Daubechies, I. (1992) Ten Lectures on Wavelets, Volume 61 of CBMS-NSF Regional Conference Series in Applied Mathematics, Philadelphia: Society for Industrial and Applied Mathematics.
5. Granger, C. W. J. and Joyeux, R. (1980) An introduction to long-memory time series models and fractional differencing. Journal of Time Series Analysis, 1, 15-29.
6. Haccou, P. and Meelis, E. (1988) Testing for the number of change points in a sequence of exponential random variables. Journal of Statistical Computation and Simulation, 30, 285-298.
7. Hinkley, D. V. (1971) Inference about the change point from cumulative sum tests. Biometrika, 58, 509-525.
8. Hosking, J. R. M. (1981) Fractional differencing. Biometrika, 68(1), 165-176.
9. Hsu, D.-A. (1977) Tests for variance shift at an unknown time point. Applied Statistics, 26(3), 279-284.
10. Inclán, C. and Tiao, G. C. (1994) Use of cumulative sums of squares for retrospective detection of changes of variance. Journal of the American Statistical Association, 89(427), 913-923.
11. Khalil, M. and Duchêne, J. (1999) Detection and classification of multiple events in piecewise stationary signals: Comparison between autoregressive and multiscale approaches. Signal Processing, 75(3), 239-251.
12. Mallat, S. (1989) A theory for multiresolution signal decomposition: The wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7), 674-693.
13. McCoy, E. J. and Walden, A. T. (1996) Wavelet analysis and synthesis of stationary long memory processes. Journal of Computational and Graphical Statistics, 5(1), 26-56.
14. Meelis, E., Bressers, M. and Haccou, P. (1991) Non-parametric testing for the number of change points in a sequence of independent random variables. Journal of Statistical Computation and Simulation, 39, 129-137.
15. Ogden, R. T. and Parzen, E. (1996) Change-point approach to data analytic wavelet thresholding. Statistics and Computing, 6(2), 93-99.
16. Percival, D. B. and Guttorp, P. (1994) Long-memory processes, the Allan variance and wavelets. In: Foufoula-Georgiou, E. and Kumar, P. (Eds.), Wavelets in Geophysics, Volume 4 of Wavelet Analysis and its Applications, pp. 325-344. San Diego: Academic Press, Inc.
17. Percival, D. B. and Mofjeld, H. O. (1997) Analysis of subtidal coastal sea level fluctuations using wavelets. Journal of the American Statistical Association, 92(439), 868-880.
18. Pettitt, N. A. (1979) A non-parametric approach to the change point problem. Applied Statistics, 28, 126-135.
19. Tewfik, A. H. and Kim, M. (1992) Correlation structure of the discrete wavelet coefficients of fractional Brownian motion. IEEE Transactions on Information Theory, 38(2), 904-909.
20. Vostrikova, L. J. (1981) Detecting 'disorder' in multidimensional random processes. Soviet Mathematics Doklady, 24, 55-59.
21. Wang, Y. (1995) Jump and sharp cusp detection by wavelets. Biometrika, 82(2), 385-397.
22. Whitcher, B., Byers, S. D., Guttorp, P. and Percival, D. B. (1998) Testing for homogeneity of variance in time series: Long memory, wavelets and the Nile River. Available for download at http://www.eurandom.tue.n1/whitcher/papers/.
23. Whitcher, B. (1998) Assessing nonstationary time series using wavelets, Ph.D. Thesis, University of Washington.