这本《时间序列分析的小波方法(英文版)》由Donald B. Percival和Andrew T. Walden所著，主要内容是：This book is an intro-duction to wavelets and their application in the analysis of discrete time series typical of those acquired in the physical sciences. While we present a thorough introduction to the basic theory behind the discrete wavelet transform (DWT), our goal is to bridge the gap between theory and practice by

 · emphasizing what the DWT actually means in practical terms;

 · showing how the DWT can be used to create informative descriptive statistics for time series analysts;

 · discussing how stochastic models can be used to assess the statistical properties of quantities computed from the DWT; and

 · presenting substantive examples of wavelet analysis of time series representative of those encountered in the physical sciences.

时间序列分析是用随机过程理论和数理统计学的方法，研究随机数据序列所遵从的统计规律，用于解决科研、工程技术、金融及经济等诸多领域内的实际问题。

这本《时间序列分析的小波方法(英文版)》由Donald B. Percival和Andrew T. Walden所著，是一本由浅入深的小波分析导论，介绍了基于小波的时间序列统计分析。实践中的离散时间技术是本书的论述重点，同时对于理解和实现离散小波变换将涉及到的诸多原理与算法也进行了详细的描述。

《时间序列分析的小波方法(英文版)》图例丰富，正文附有大量练习，并在附录中给出了练习的答案。每章另备有适于课堂布置的练习。本书网站有所用时间序列与小波的材料，并可以得到用S-Plus和其他语言开发软件的信息。

Preface

Conventions and Notation

1. Introduction to Wavelets

 1.0 Introduction

 1.1 The Essence of a Wavelet

Comments and Extensions to Section 1.1

 1.2 The Essence of Wavelet Analysis

Comments and Extensions to Section 1.2

 1.3 Beyond the CWT: the Discrete Wavelet Transform

Comments and Extensions to Section 1.3

2. Review of Fourier Theory and Filters

 2.0 Introduction

 2.1 Complex Variables and Complex Exponentials

 2.2 Fourier Transform of Infinite Sequences

 2.3 Convolution/Filtering of Infinite Sequences

 2.4 Fourier Transform of Finite Sequences

 2.5 Circular Convolution/Filtering of Finite Sequences

 2.6 Periodized Filters

Comments and Extensions to Section 2.6

 2.7 Summary of FoUrier Theory

 2.8 Exercises

3. Orthonormal Transforms of Time Series

 3.0 Introduction

 3.1 Basic Theory for Orthonormal Transforms

 3.2 The Projection Theorem :

 3.3 Complex-Valued Transforms

 3.4 The Orthonormal Discrete Fourier Transform

Comments and Extensions to Section 3.4

 3.5 Summary

 3.6 Exercises

4. The Discrete Wavelet Transform

 4.0 Introduction

 4.1 Qualitative Description of the DWT

Key Facts and Definitions in Section 4.1

Comments and Extensions to Section 4.1

 4.2 The Wavelet Filter

Key Facts and Definitions in Section 4.2

Comments and Extensions to Section 4.2

 4.3 The Scaling Filter

Key Facts and Definitions in Section 4.3

Comments and Extensions to Section 4.3

 4.4 First Stage of the Pyramid Algorithm

Key Facts and Definitions in Section 4.4

Comments and Extensions to Section 4.4

 4.5 Second Stage of the Pyramid Algorithm

Key Facts and Definitions in Section 4.5

 4.6 General Stage of the Pyramid Algorithm

Key Facts and Definitions in Section 4.6

Comments and Extensions to Section 4.6

 4.7 The Partial Discrete Wavelet Transform

 4.8 Daubechies Wavelet and Scaling Filters: Form and Phase

Key Facts and Definitions in Section 4.8

Comments and Extensions to Section 4.8

 4.9 Coiflet Wavelet and Scaling Filters: Form and Phase

 4.10 Example: Electrocardiogram Data

Comments and Extensions to Section 4.10

 4.11 Practical Considerations

Comments and Extensions to Section 4.11

 4.12 Summary

 4.13 Exercises

5. The Maximal Overlap DisCrete Wavelet Transform

 5.0 Introduction

 5.1 Effect of Circular Shifts on the DWT

 5.2 MODWT Wavelet and Scaling Filters

 5.3 Basic Concepts for MODWT

Key Facts and Definitions in Section 5.3

 5.4 Definition of jth Level MODWT Coefficients

Key Facts and Definitions in Section 5.4

Comments and Extensions to Section 5.4

 5.5 Pyramid Algorithm for the MODWT

Key Facts and Definitions in Section 5.5

Comments and Extensions to Section 5.5

 5.6 MODWT Analysis of 'Bump' Time Series

 5.7 Example: Electrocardiogram Data

 5.8 Example: Subtidal Sea Level Fluctuations

 5.9 Example: Nile River Minima

 5.10 Example: Ocean Shear Measurements

 5.11 Practical Considerations

 5.12 Summary

 5.13 Exercises

6. The Discrete Wavelet Packet Transform

 6.0 Introduction

 6.1 Basic Concepts

Comments and Extensions to Section 6.1

 6.2 Example: DWPT of Solar Physics Data

 6.3 The Best Basis Algorithm

Comments and Extensions to Section 6.3

 6.4 Example: Best Basis for Solar Physics Data

 6.5 Time Shifts for Wavelet Packet Filters

Comments and Extensions to Section 6.5

 6.6 Maximal Overlap Discrete Wavelet Packet Transform

 6.7 Example: MODWPT of Solar Physics Data

 6.8 Matching Pursuit

 6.9 Example: Subtidal Sea Levels

Comments and Extensions to Section 6.9

 6.10 Summary

 6.11 Exercises

7. Random Variables and Stochastic Processes

 7.0 Introduction

 7.1 Univariate Random Variables and PDFs

 7.2 Random Vectors and PDFs

 7.3 A Bayesian Perspective

 7.4 Stationary Stochastic Processes

 7.5 Spectral Density Estimation

Comments and Extensions to Section 7.5

 7.6 Definition and Models for Long Memory Processes

Comments and Extensions to Section 7.6

 7.7 Nonstationary 1/f-Type Processes

Comments and Extensions to Section 7.7

 7.8 Simulation of Stationary Processes

Comments and Extensions to Section 7.8

 7.9 Simulation of Stationary Autoregressive Processes

 7.10 Exercises

8. The Wavelet Variance

 8.0 Introduction

 8.1 Definition and Rationale for the Wavelet Variance

Comments and Extensions to Section 8.1

 8.2 Basic Properties of the Wavelet Variance

Comments and Extensions to Section 8.2

 8.3 Estimation of the Wavelet Variance

Comments and Extensions to Section 8.3

 8.4 Confidence Intervals for the Wavelet Variance

Comments and Extensions to Section 8.4

 8.5 Spectral Estimation via the Wavelet Variance

Comments and Extensions to Section 8.5

 8.6 Example: Atomic Clock Deviates

 8.7 Example: Subtidal Sea Level Fluctuations

 8.8 Example: Nile River Minima

 8.9 Example: Ocean Shear Measurements

 8.10 Summary

 8.11 Exercises

9. Analysis and Synthesis of Long Memory Processes

 9.0 Introduction

 9.1 Discrete Wavelet Transform of a Long Memory Process

Comments and Extensions to Section 9.1

 9.2 Simulation of a Long Memory Process

Comments and Extensions to Section 9.2

 9.3 MLEs for Stationary FD Processes

Comments and Extensions to Section 9.3

 9.4 MLEs for Stationary or Nonstationary FD Processes

Comments and Extensions to Section 9.4

 9.5 Least Squares Estimation for FD Processes

Comments and Extensions to Section 9.5

 9.6 Testing for Homogeneity of Variance

Comments and Extensions to Section 9.6

 9.7 Example: Atomic Clock Deviates

 9.8 Example: Nile River Minima

 9.9 Summary

 9.10 Exercises

10. Wavelet-Based Signal Estimation

 10.0 Introduction

 10.1 Signal Representation via Wavelets

 10.2 Signal Estimation via Thresholding

 10.3 Stochastic Signal Estimation via Scaling

 10.4 Stochastic Signal Estimation via Shrinkage

Comments and Extensions to Section 10.4

 10.5 IID Gaussian Wavelet Coefficients

Comments and Extensions to Section 10.5

 10.6 Uncorrelated Non-Gaussian Wavelet Coefficients

Comments and Extensions to Section 10.6

 10.7 Correlated Gaussian Wavelet Coefficients

Comments and Extensions to Section 10.7

 10.8 Clustering and Persistence of Wavelet Coefficients ...

 10.9 Summary

 10.10 Exercises

11. Wavelet Analysis of Finite Energy Signals

 11.0 Introduction

 11.1 Translation and Dilation

 11.2 Scaling Functions and Approximation Spaces

Comments and Extensions to Section 11.2

 11.3 Approximation of Finite Energy Signals

Comments and Extensions to Section 11.3

 11.4 Two-Scale Relationships for Scaling Functions

 11.5 Scaling Functions and Scaling Filters

Comments and Extensions to Section 11.5

 11.6 Wavelet Functions and Detail Spaces

 11.7 Wavelet Functions and Wavelet Filters

 11.8 Multiresolution Analysis of Finite Energy Signals

 11.9 Vanishing Moments

Comments and Extensions to Section 11.9

 11.10 Spectral Factorization and Filter Coefficients

Comments and Extensions to Section 11.10

 11.11 Summary

 11.12 Exercises

Appendix. Answers to Embedded Exercises

References

Author Index

Subject Index