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

Book Description

An Introduction to Wavelets and Other Filtering Methods in Finance and Economics presents a unified view of filtering techniques with a special focus on wavelet analysis in finance and economics. It emphasizes the methods and explanations of the theory that underlies them. It also concentrates on exactly what wavelet analysis (and filtering methods in general) can reveal about a time series. It offers testing issues which can be performed with wavelets in conjunction with the multi-resolution analysis. The descriptive focus of the book avoids proofs and provides easy access to a wide spectrum of parametric and nonparametric filtering methods. Examples and empirical applications will show readers the capabilities, advantages, and disadvantages of each method.

*The first book to present a unified view of filtering techniques

*Concentrates on exactly what wavelets analysis and filtering methods in general can reveal about a time series

*Provides easy access to a wide spectrum of parametric and non-parametric filtering methods

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Dedication
  6. LIST OF FIGURES
  7. LIST OF TABLES
  8. ACKNOWLEDGMENTS
  9. PREFACE
  10. Chapter 1: INTRODUCTION
    1. 1.1 FOURIER VERSUS WAVELET ANALYSIS
    2. 1.2 SEASONALITY FILTERING
    3. 1.3 DENOISING
    4. 1.4 IDENTIFICATION OF STRUCTURAL BREAKS
    5. 1.5 SCALING
    6. 1.6 AGGREGATE HETEROGENEITY AND TIMESCALES
    7. 1.7 MULTISCALE CROSS-CORRELATION
    8. 1.8 OUTLINE
  11. Chapter 2: LINEAR FILTERS
    1. 2.1 INTRODUCTION
    2. 2.2 FILTERS IN TIME DOMAIN
    3. 2.3 FILTERS IN THE FREQUENCY DOMAIN
    4. 2.4 FILTERS IN PRACTICE
  12. Chapter 3: OPTIMUM LINEAR ESTIMATION
    1. 3.1 INTRODUCTION
    2. 3.2 THE WIENER FILTER AND ESTIMATION
    3. 3.3 RECURSIVE FILTERING AND THE KALMAN FILTER
    4. 3.4 PREDICTION WITH THE KALMAN FILTER
    5. 3.5 VECTOR KALMAN FILTER ESTIMATION
    6. 3.6 APPLICATIONS
  13. Chapter 4: DISCRETE WAVELET TRANSFORMS
    1. 4.1 INTRODUCTION
    2. 4.2 PROPERTIES OF THE WAVELET TRANSFORM
    3. 4.3 DISCRETE WAVELET FILTERS
    4. 4.4 THE DISCRETE WAVELET TRANSFORM
    5. 4.5 THE MAXIMAL OVERLAP DISCRETE WAVELET TRANSFORM
    6. 4.6 PRACTICAL ISSUES IN IMPLEMENTATION
    7. 4.7 APPLICATIONS
  14. Chapter 5: WAVELETS AND STATIONARY PROCESSES
    1. 5.1 INTRODUCTION
    2. 5.2 WAVELETS AND LONG-MEMORY PROCESSES
    3. 5.3 GENERALIZATIONS OF THE DWT AND MODWT
    4. 5.4 WAVELETS AND SEASONAL LONG MEMORY
    5. 5.5 APPLICATIONS
  15. Chapter 6: WAVELET DENOISING
    1. 6.1 INTRODUCTION
    2. 6.2 NONLINEAR DENOISING VIA THRESHOLDING
    3. 6.3 THRESHOLD SELECTION
    4. 6.4 IMPLEMENTING WAVELET DENOISING
    5. 6.5 APPLICATIONS
  16. Chapter 7: WAVELETS FOR VARIANCE-COVARIANCE ESTIMATION
    1. 7.1 INTRODUCTION
    2. 7.2 THE WAVELET VARIANCE
    3. 7.3 TESTING HOMOGENEITY OF VARIANCE
    4. 7.4 THE WAVELET COVARIANCE AND CROSS-COVARIANCE
    5. 7.5 THE WAVELET CORRELATION AND CROSS-CORRELATION
    6. 7.6 APPLICATIONS
    7. 7.7 UNIVARIATE AND BIVARIATE SPECTRUM ANALYSIS
  17. Chapter 8: ARTIFICIAL NEURAL NETWORKS
    1. 8.1 INTRODUCTION
    2. 8.2 ACTIVATION FUNCTIONS
    3. 8.3 FEEDFORWARD NETWORKS
    4. 8.4 RECURRENT NETWORKS
    5. 8.5 NETWORK SELECTION
    6. 8.6 ADAPTIVITY
    7. 8.7 ESTIMATION OF RECURRENT NETWORKS
    8. 8.8 APPLICATIONS OF NEURAL NETWORK MODELS
  18. NOTATIONS
  19. BIBLIOGRAPHY
  20. INDEX