Wavelet Methods for Time Series AnalysisCambridge University Press, 24 лип. 2000 р. - 594 стор. 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 |
Зміст
Introduction to Wavelets | 1 |
Review of Fourier Theory and Filters | 20 |
Orthonormal Transforms of Time Series | 41 |
The Discrete Wavelet Transform | 56 |
The Maximal Overlap Discrete Wavelet Transform | 159 |
The Discrete Wavelet Packet Transform | 206 |
Random Variables and Stochastic Processes | 255 |
The Wavelet Variance | 295 |
Analysis and Synthesis of Long Memory Processes | 340 |
WaveletBased Signal Estimation | 393 |
Wavelet Analysis of Finite Energy Signals | 457 |
Appendix Answers to Embedded Exercises | 501 |
| 552 | |
Author Index | 565 |
Інші видання - Показати все
Wavelet Methods for Time Series Analysis Donald B. Percival,Andrew T. Walden Обмежений попередній перегляд - 2000 |
Wavelet Methods for Time Series Analysis Donald B. Percival,Andrew T. Walden Обмежений попередній перегляд - 2006 |
Wavelet Methods for Time Series Analysis Donald B. Percival,Andrew T. Walden Попередній перегляд недоступний - 2000 |
Загальні терміни та фрази
Allan variance analysis Answer to Exercise approximation average circular filter circularly shifted coiflet Comments and Extensions compute corresponding D₁ Daubechies Daubechies wavelet decomposition defined discrete Fourier transform discrete wavelet transform DWPT DWT coefficients elements Equation example Extensions to Section FD process filter h1 Fourier transform frequency Gaussian given ğı h₁ Haar wavelet hence integer jth level likelihood function linear long memory process matching pursuit matrix MODWT MODWT wavelet multiresolution analysis multitaper noise nonzero Note obtain ODFT orthonormal transform parameter partial DWT periodogram pyramid algorithm real-valued RMSE rows sample mean scaling coefficients scaling filter SDF estimate sequence shows signal simulated squared gain function stationary process thresholding transfer function transform coefficients V₁ values variability vector W₁ wavelet and scaling wavelet coefficients wavelet filter wavelet variance width Wj,t yields zero mean