Wavelet Methods for Time Series Analysis

This book contains detailed descriptions of the theory and algorithms needed to understand and implement discrete wavelet transforms.

Donald B. Percival (Author), Andrew T. Walden (Author)

9780521685085, Cambridge University Press

Paperback, published 27 February 2006

622 pages, 24 tables 119 exercises
25.5 x 17.8 x 2.9 cm, 1.066 kg

'The authors … provide considerable background material, tell their story from scratch, proceed at a careful pace … and work out detailed applications … Recommended.' Choice

This introduction to wavelet analysis 'from the ground level and up', and to wavelet-based statistical analysis of time series focuses on practical discrete time techniques, with detailed descriptions of the theory and algorithms needed to understand and implement the discrete wavelet transforms. Numerous examples illustrate the techniques on actual time series. The many embedded exercises - with complete solutions provided in the Appendix - allow readers to use the book for self-guided study. Additional exercises can be used in a classroom setting. A Web site offers access to the time series and wavelets used in the book, as well as information on accessing software in S-Plus and other languages. Students and researchers wishing to use wavelet methods to analyze time series will find this book essential.

1. Introduction to wavelets
2. Review of Fourier theory and filters
3. Orthonormal transforms of time series
4. The discrete wavelet transform
5. The maximal overlap discrete wavelet transform
6. The discrete wavelet packet transform
7. Random variables and stochastic processes
8. The wavelet variance
9. Analysis and synthesis of long memory processes
10. Wavelet-based signal estimation
11. Wavelet analysis of finite energy signals
Appendix. Answers to embedded exercises
References
Author index
Subject index.

Subject Areas: Computer networking & communications [UT], Probability & statistics [PBT]