A step-by-step introduction to modeling, training, and forecasting using wavelet networks Wavelet Neural Networks: With Applications in Financial Engineering, Chaos, and Classification presents the statistical model identification framework that is needed to successfully apply wavelet networks as well as extensive comparisons of alternate methods. Providing a concise and rigorous treatment for constructing optimal wavelet networks, the book links mathematical aspects of wavelet network construction to statistical modeling and forecasting applications in areas such as finance, chaos, and classification. The authors ensure that readers obtain a complete understanding of model identification by providing in-depth coverage of both model selection and variable significance testing. Featuring an accessible approach with introductory coverage of the basic principles of wavelet analysis, Wavelet Neural Networks: With Applications in Financial Engineering, Chaos, and Classification also includes: • Methods that can be easily implemented or adapted by researchers, academics, and professionals in identification and modeling for complex nonlinear systems and artificial intelligence • Multiple examples and thoroughly explained procedures with numerous applications ranging from financial modeling and financial engineering, time series prediction and construction of confidence and prediction intervals, and classification and chaotic time series prediction • An extensive introduction to neural networks that begins with regression models and builds to more complex frameworks • Coverage of both the variable selection algorithm and the model selection algorithm for wavelet networks in addition to methods for constructing confidence and prediction intervals Ideal as a textbook for MBA and graduate-level courses in applied neural network modeling, artificial intelligence, advanced data analysis, time series, and forecasting in financial engineering, the book is also useful as a supplement for courses in informatics, identification and modeling for complex nonlinear systems, and computational finance. In addition, the book serves as a valuable reference for researchers and practitioners in the fields of mathematical modeling, engineering, artificial intelligence, decision science, neural networks, and finance and economics.

Table of Contents:
Preface xiii 1 Machine Learning and Financial Engineering 1 Financial Engineering 2 Financial Engineering and Related Research Areas 3 Functions of Financial Engineering 5 Applications of Machine Learning in Finance 6 From Neural to Wavelet Networks 8 Wavelet Analysis 8 Extending the Fourier Transform: The Wavelet Analysis Paradigm 10 Neural Networks 17 Wavelet Neural Networks 19 Applications of Wavelet Neural Networks in Financial Engineering, Chaos, and Classification 21 Building Wavelet Networks 23 Variable Selection 23 Model Selection 24 Model Adequacy Testing 25 Book Outline 25 References 27 2 Neural Networks 35 Parallel Processing 36 Processing Units 37 Activation Status and Activation Rules 37 Connectivity Model 39 Perceptron 41 The Approximation Theorem 42 The Delta Rule 42 Backpropagation Neural Networks 44 Multilayer Feedforward Networks 44 The Generalized Delta Rule 45 Backpropagation in Practice 49 Training with Backpropagation 51 Network Paralysis 54 Local Minima 54 Nonunique Solutions 56 Configuration Reference 56 Conclusions 59 References 59 3 Wavelet Neural Networks 61 Wavelet Neural Networks for Multivariate Process Modeling 62 Structure of a Wavelet Neural Network 62 Initialization of the Parameters of the Wavelet Network 64 Training a Wavelet Network with Backpropagation 69 Stopping Conditions for Training 72 Evaluating the Initialization Methods 73 Conclusions 77 References 78 4 Model Selection: Selecting the Architecture of the Network 81 The Usual Practice 82 Early Stopping 82 Regularization 83 Pruning 84 Minimum Prediction Risk 86 Estimating the Prediction Risk Using Information Criteria 87 Estimating the Prediction Risk Using Sampling Techniques 89 Bootstrapping 91 Cross-Validation 94 Model Selection Without Training 95 Evaluating the Model Selection Algorithm 97 Case 1: Sinusoid and Noise with Decreasing Variance 98 Case 2: Sum of Sinusoids and Cauchy Noise 100 Adaptive Networks and Online Synthesis 103 Conclusions 104 References 105 5 Variable Selection: Determining the Explanatory Variables 107 Existing Algorithms 108 Sensitivity Criteria 110 Model Fitness Criteria 112 Algorithm for Selecting the Significant Variables 114 Resampling Methods for the Estimation of Empirical Distributions 116 Evaluating the Variable Significance Criteria 117 Case 1: Sinusoid and Noise with Decreasing Variance 117 Case 2: Sum of Sinusoids and Cauchy Noise 120 Conclusions 123 References 123 6 Model Adequacy: Determining a Network’s Future Performance 125 Testing the residuals 126 Testing for Serial Correlation in the Residuals 127 Evaluation Criteria for the Prediction Ability of the Wavelet Network 129 Measuring the Accuracy of the Predictions 129 Scatter Plots 131 Linear Regression Between Forecasts and Targets 132 Measuring the Ability to Predict the Change in Direction 136 Two Simulated Cases 137 Case 1: Sinusoid and Noise with Decreasing Variance 137 Case 2: Sum of Sinusoids and Cauchy Noise 142 Classification 146 Assumptions and Objectives of Discriminant Analysis 146 Validation of the Discriminant Function 148 Evaluating the Classification Ability of a Wavelet Network 150 Case 3: Classification Example on Bankruptcy 153 Conclusions 156 References 156 7 Modeling Uncertainty: From Point Estimates to Prediction Intervals 159 The Usual Practice 160 Confidence and Prediction Intervals 161 Constructing Confidence Intervals 164 The Bagging Method 164 The Balancing Method 165 Constructing Prediction Intervals 166 The Bagging Method 167 The Balancing Method 168 Evaluating the Methods for Constructing Confidence and Prediction Intervals 168 Conclusions 170 References 171 8 Modeling Financial Temperature Derivatives 173 Weather Derivatives 174 Pricing and Modeling Methods 175 Data Description and Preprocessing 176 Data Examination 176 Model for the Daily Average Temperature: Gaussian Ornstein–Uhlenbeck Process with Lags and Time-Varying Mean Reversion 179 Estimation Using Wavelet Networks 183 Variable Selection 183 Model Selection 187 Initialization and Training 187 Confidence and Prediction Intervals 189 Out-of-Sample Comparison 189 Conclusions 191 References 192 9 Modeling Financial Wind Derivatives 197 Modeling the Daily Average Wind Speed 199 Linear ARMA Model 202 Wavelet Networks for Wind Speed Modeling 206 Variable Selection 206 Model Selection 209 Initialization and Training 209 Model Adequacy 209 Speed of Mean Reversion and Seasonal Variance 211 Forecasting Daily Average Wind Speeds 212 Conclusions 215 References 216 10 Predicting Chaotic Time Series 219 Mackey–Glass Equation 220 Model Selection 221 Initialization and Training 221 Model Adequacy 222 Predicting the Evolution of the Chaotic Mackey–Glass Time Series 225 Confidence and Prediction Intervals 226 Conclusions 228 References 229 11 Classification of Breast Cancer Cases 231 Data 232 Part A: Classification of Breast Cancer 232 Model Selection 232 Initialization and Training 233 Classification 233 Part B: Cross-Validation in Breast Cancer Classification in Wisconsin 235 Variable Selection 235 Model Selection 237 Initialization and Training 238 Classification Power of the Full and Reduced Models 238 Part C: Classification of Breast Cancer (Continued) 241 Classification 241 Conclusions 243 References 244 Index 245