An Introduction to Wavelets and Other Filtering Methods in Finance and Economics

Preface.
Notations.

1. Introduction

1.1 Fourier versus Wavelet Analysis

1.2 Seasonality Filtering

1.3 Denoising

1.4 Identification of Structural Breaks

1.5 Scaling

1.6 Aggregate Heterogeneity and Time Scales

1.7 Multiscale Cross-Correlation

1.8 Outline

2. Linear Filters

2.1 Introduction

2.2 Filters in Time Domain

2.3 Filters in the Frequency Domain

2.3 Filters in Practice

3. Optimum Linear Estimation

3.1 Introduction

3.2 The Wiener Filter and Estimation

3.3 Recursive Filtering and the Kalman Filter

3.4 Prediction with the Kalman Filter

3.5 Vector Kalman Filter Estimation

3.6 Applications

4. Discrete Wavelet Transforms

4.1 Introduction

4.2 Properties of the Wavelet Transform

4.3 Discrete Wavelet Filters

4.4 The Discrete Wavelet Transform

4.5 The Maximal Overlap Discrete Wavelet Transform

4.6 Practical Issues in Implementation

4.7 Applications

5. Wavelets and Stationary Processes

5.1 Introduction

5.2 Wavelets and Long-Memory Processes

5.3 Generalizations of the DWT and MODWT

5.4 Wavelets and Seasonal Long Memory

5.5 Applications

6. Wavelet Denoising

6.1 Introduction

6.2 Nonlinear Denoising via Thresholding

6.3 Threshold Selection

6.4 Implementing Wavelet Denoising

6.5 Applications

7. Wavelets for Variance-Covariance Estimation

7.1 Introduction

7.2 The Wavelet Variance

7.3 Testing Homogeneity of Variance

7.4 The Wavelet Covariance and Cross-Covariance

7.5 The Wavelet Correlation and Cross-Correlation

7.6 Applications

7.7 Univariate and Bivariate Spectrum Analysis

8. Artificial Neural Networks

8.1 Introduction

8.2 Activation Functions

8.3 Feedforward Networks

8.4 Recurrent Networks

8.5 Network Selection

8.6 Adaptivity

8.7 Estimation of Recurrent Networks

8.8 Applications of Neural Network Models
Notations
Bibliography
Index