Wavelet packet methods for the analysis of variance of time series with application to crack widths on the Brunelleschi dome

Journal of Computational and Graphical Statistics

Volumn 13, Issue 3, 2004, Pages 639-658

  Gabbanini, Francesco ^a   Vannucci, Marina ^b   Bartoli, Gianni ^a   Moro, Antonio ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Change points detection; Nondecimated transforms; Wavelet variance

Indexed keywords

EID: 4344684047     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/106186004X2372     Document Type: Article

References (21)

1. Bollerslev, T. (1986), "Generalized Autoregressive Conditional Heteroskedasticity," Journal of Econometrics, 31, 307-327.
2. Box, G. E. P., Jenkins, G. M., and Reinsei, G. C. (1994), Time Series Analysis: Forecasting and Control (3rd ed.), Englewood Cliffs, NJ: Prentice Hall.
3. Chiarugi, A., Fanelli, M., and Giuseppetti, G. (1983), "Analysis of a Brunelleschi-Type Dome Including Thermal Loads," in IABSE Symposium on Strengthening of Building Structure, Diagnosis and Therapy, Zurich, pp. 169-178.
4. Coifman, R. R., and Donoho, D. (1995), "Time Invariant Wavelet Denoising," in Wavelets and Statistics, eds. A. Antoniadis and G. Oppenheim, Lecture Notes in Statistics, vol. 103, New York: Springer, pp. 125-150.
5. Daubechies, I. (1992), Ten Lectures on Wavelets (vol. 61), Philadelphia: SIAM.
6. Engle, R. F. (1982), "Autoregressive Conditional Heteroskedasticity With Estimates of the Variance of United Kingdom Inflation," Econometrics, 50, 987-1007.
7. Gabbanini, F. (2002), "Analisi dei dati Provenienti dal Sistema di Monitoraggio Installato Sulla Cupola di Santa Maria del Fiore," unpublished Ph.D. thesis, Department of Statistics, University of Florence, Italy.
8. Inclàn, C., and Tiao, G. C. (1994), "Use of Cumulative Sums of Squares for Retrospective Detection of Changes in Variance," Journal of the American Statistical Association, 89, 913-923.
9. Mallat, S. G. (1989), "A Theory of Multiresolution Signal Decomposition: The Wavelet Representation," IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 674-693.
10. Nason, G. P., and Silverman, B. W. (1995), "The Stationary Wavelet Transform and Some Statistical Applications," in Wavelets and Statistics, eds. A. Antoniadis and G. Oppenheim, Lecture Notes in Statistics, vol. 103, New York: Springer, pp. 281-300.
11. Percival, D. B. (1995), "On the Estimation of the Wavelet Variance," Biometrika, 82, 619-631.
12. Percival, D. B., and Mofjeld, H. (1997), "Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets," Journal of the American Statistical Association, 92, 868-880.
13. Percival, D. B., and Walden, A. T. (2000), Wavelet Methods for Time Series Analysis, Cambridge: Cambridge University Press.
14. Percival, D. B., Sardy, S., and Davison, A. C. (2000), "Wavestrapping Time Series: Adaptive Wavelet-Based Bootstrapping," in Nonlinear and Nonstationary Signal Processing, eds. B. J. Fitzgerald, R. L. Smith, A. T. Walden, and P. C. Young, Cambridge, UK: Cambridge University Press.
15. Serroukh, A., Walden, A. T., and Percival, D. B. (2000), "Statistical Properties and Uses of the Wavelet Variance Estimator for the Scale Analysis of Time Series," Journal of the American Statistical Association, 95, 184-196.
16. Shensa, G. (1992), "The: Discrete Wavelet Transform: Wedding the à trous and Mallat Algorithms," IEEE Transactions on Signal Processing, 40, 2464-2482.
17. Tewfik, A. H., and Kim, M. (1992), "Correlation Structure of the Discrete Wavelet Coefficients of Fractional Brownian Motion," IEEE Transactions on Information Theory, 38, 904-909.
18. Walden, A. T., and Contreras Cristan, A. (1998), "The Phase-Corrected Undecimated Discrete Wavelet Packet Transform and its Application to Interpreting the Timing of Events," Proceedings of the Royal Society of London, A, 454, pp. 2243-2266.
19. Whitcher, B., Byers, S. D., Guttorp, P., and Percival, D. B. (2002), "Testing for Homogeneity of Variance in Time Series: Long Memory, Wavelets and the Nile River," Water Resources Research, 38, 10.1029/2001WR000509.
20. Whitcher, B., Guttorp, P., and Percival, D. B. (2000), "Multiscale Detection and Location of Multiple Variance Changes in the Presence of Long Memory," Journal of Statistical Computation and Simulation, 68, 65-88.
21. Wickerhauser, M. V. (1994), Adapted Wavelet Analysis from Theory to Software Algorithms, Wellesley, MA: AK Peters.