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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.
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
