Wavelet Methods for Time Series Analysis

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.

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.

This introduction to wavelet analysis and 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. The book contains numerous exercises and a website offering access to the time series and wavelet software.