Wavelet methods for time series analysis

Author: (USA) Percival
Publisher:
Publish Date: 2006-03-01
Features: Time series analysis is the use of stochastic process theory and mathematical statistics methods to study the statistical laws that random data sequences follow, and it is used to solve practical problems in many fields such as scientific research, engineering technology, finance, and economics. This book is an introduction to wavelet analysis that progresses from basic to advanced levels, introducing time series statistical analysis based on wavelets. Practical discrete-time techniques are the focus of the book, while it also provides a detailed description of the principles and algorithms involved in understanding and implementing discrete wavelet transform. The book thoroughly introduces the application of wavelet methods in time series analysis, with abundant examples, clear and concise language, and rigorous arguments. Additionally, the book offers a concise and practical explanation of the mathematical knowledge required for wavelet analysis, embeds numerous exercises within the text, and provides answers to these exercises in the appendix. Each chapter also includes exercises suitable for classroom assignments. This book is suitable as a textbook for students majoring in statistics, mathematics, and related fields at universities, as well as a reference book for researchers in related fields. The book thoroughly introduces the application of wavelet methods in time series analysis, explains the mathematical knowledge required for wavelet analysis, and embeds numerous exercises and answers within the text. The book consists of 11 chapters, including an introduction to wavelets, orthogonal transformations of time series, discrete wavelet packet transform, and more.