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

Contents

• Dedication
• Acknowledgments
• Preface

• Filters in Time Domain 16
• Filters in the Frequency Domain 25
• Filters in Practice 39

• The Wiener Filter and Estimation 54
• Recursive Filtering and the Kalman Filter 63
• Prediction with the Kalman Filter 71
• Vector Kalman Filter Estimation 74
• Applications 80

• Properties of the Wavelet Transform 101
• Discrete Wavelet Filters 106
• The Discrete Wavelet Transform 117
• The Maximal Overlap Discrete Wavelet Transform 134
• Practical Issues in Implementation 143
• Applications 146

• Wavelets and Long-Memory Processes 162
• Generalizations of the DWT and MODWT 176
• Wavelets and Seasonal Long Memory 183
• Applications 194

• Nonlinear Denoising via Thresholding 207
• Threshold Selection 212
• Implementing Wavelet Denoising 224
• Applications 227

• The Wavelet Variance 238
• Testing Homogeneity of Variance 246
• The Wavelet Covariance and Cross-Covariance 251
• The Wavelet Correlation and Cross-Correlation 256
• Applications 262
• Univariate and Bivariate Spectrum Analysis 266

• Activation Functions 276
• Feedforward Networks 279
• Recurrent Networks 290
• Network Selection 294
• Adaptivity 301
• Estimation of Recurrent Networks 301
• Applications of Neural Network Models 303
• Notations 315
• Bibliography 323
• Index 349