时间序列分析的小波方法：英文版

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
Comments and Extensions to 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 Nonstationry 1/f-Type Processes
Comments and Extensions to Section 7.7
7.8 Simulation of Stationary Process
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 Wvelets
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