Wavelet Methods for Time Series Analysis (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 4
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
Why Read This Book
You should read this book if you need a rigorous, practical treatment of wavelet methods applied to real-world time series: you will get clear explanations of the discrete wavelet transform (DWT/MODWT), estimation and inference techniques, and many worked examples with code so you can apply methods directly. The book balances algorithmic detail with statistical interpretation so you can both implement transforms and make sound inferences about nonstationary signals.
Who Will Benefit
Graduate students, researchers, and DSP engineers working on time-series analysis, spectral estimation, denoising, or time-frequency methods who need a statistically principled, implementable wavelet toolkit.
Level: Advanced — Prerequisites: Familiarity with signals and systems (Fourier analysis), linear algebra, and basic probability/statistics; programming experience (R/S-Plus or MATLAB) helpful.
Key Takeaways
- Implement the discrete wavelet transform (DWT) and maximal-overlap DWT (MODWT) and understand their numerical properties.
- Estimate wavelet variance and wavelet-based spectra to analyze scale-dependent behavior in time series.
- Perform statistical inference with wavelet coefficients, including confidence intervals and hypothesis testing for spectral features.
- Apply wavelet denoising and thresholding methods to remove noise while preserving transient features.
- Use provided algorithms and example code (S-Plus/R and MATLAB) to reproduce and adapt analyses on real datasets.
Topics Covered
- 1. Introduction and motivation: wavelets for time series
- 2. Basics of discrete wavelet transforms and multiresolution analysis
- 3. The DWT, MODWT and boundary handling for time series
- 4. Wavelet variance and scale-dependent second-order properties
- 5. Estimation and inference for wavelet-based spectra
- 6. Time-frequency methods and local stationarity
- 7. Wavelet-based denoising and threshold selection
- 8. Practical algorithms, implementation issues and numerical examples
- 9. Case studies and applications to real time series
- 10. Exercises and worked solutions
- Appendices: mathematical background, probability results, and software notes
Languages, Platforms & Tools
How It Compares
More focused on time-series statistics than Mallat's A Wavelet Tour of Signal Processing (which is broader DSP/theory); more applied-statistics oriented than Vidakovic's Statistical Modeling by Wavelets and provides more implementation guidance and time-series-specific inference.
