Wavelet Methods for Time Series Analysis

by Donald B. Percival, Andrew T. Walden

Overview

The analysis of time series data is essential to many areas of science, engineering, finance and economics. 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. Author resource page: http://faculty.washington.edu/dbp/wmtsa.html

Product Details

ISBN-13:	9780521685085
Publisher:	Cambridge University Press
Publication date:	02/27/2006
Series:	Cambridge Series in Statistical and Probabilistic Mathematics , #4
Edition description:	New Edition
Pages:	622
Product dimensions:	7.01(w) x 10.04(h) x 1.14(d)

Table of Contents

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.

Editorial Reviews

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

From the Publisher

An applied physicist and a mathematician introduce the topic of wavelets and their applications in the analysis of discrete time series typical of those acquired in the physical sciences. Emphasizing the practical meaning of discrete wavelet transform (DWT), they show how it can be used to create informative descriptive statistics for time series analysts; discuss how stochastic models can be used to assess the statistical properties of quantities computed from the DWT; and present examples of wavelet analysis of time series representative of those encountered in the physical sciences. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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