Neural Networks in Finance: Gaining Predictive Edge in the Market

Contents
Preface xi
1 Introduction 1
1.1 Forecasting, Classification, and Dimensionality
Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Synergies . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 The Interface Problems . . . . . . . . . . . . . . . . . . . 6
1.4 Plan of the Book . . . . . . . . . . . . . . . . . . . . . . 8
I Econometric Foundations 11
2 What Are Neural Networks? 13
2.1 Linear Regression Model . . . . . . . . . . . . . . . . . . 13
2.2 GARCH Nonlinear Models . . . . . . . . . . . . . . . . . 15
2.2.1 Polynomial Approximation . . . . . . . . . . . . . 17
2.2.2 Orthogonal Polynomials . . . . . . . . . . . . . . . 18
2.3 Model Typology . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 What Is A Neural Network? . . . . . . . . . . . . . . . . 21
2.4.1 Feedforward Networks . . . . . . . . . . . . . . . . 21
2.4.2 Squasher Functions . . . . . . . . . . . . . . . . . 24
2.4.3 Radial Basis Functions . . . . . . . . . . . . . . . 28
2.4.4 Ridgelet Networks . . . . . . . . . . . . . . . . . . 29
2.4.5 Jump Connections . . . . . . . . . . . . . . . . . . 30
2.4.6 Multilayered Feedforward Networks . . . . . . . . 32
2.4.7 Recurrent Networks . . . . . . . . . . . . . . . . . 34
2.4.8 Networks with Multiple Outputs . . . . . . . . . . 36
2.5 Neural Network Smooth-Transition Regime Switching
Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.5.1 Smooth-Transition Regime Switching Models . . . 38
2.5.2 Neural Network Extensions . . . . . . . . . . . . . 39
2.6 Nonlinear Principal Components: Intrinsic
Dimensionality . . . . . . . . . . . . . . . . . . . . . . . . 41
2.6.1 Linear Principal Components . . . . . . . . . . . . 42
2.6.2 Nonlinear Principal Components . . . . . . . . . . 44
2.6.3 Application to Asset Pricing . . . . . . . . . . . . 46
2.7 Neural Networks and Discrete Choice . . . . . . . . . . . 49
2.7.1 Discriminant Analysis . . . . . . . . . . . . . . . . 49
2.7.2 Logit Regression . . . . . . . . . . . . . . . . . . . 50
2.7.3 Probit Regression . . . . . . . . . . . . . . . . . . 51
2.7.4 Weibull Regression . . . . . . . . . . . . . . . . . 52
2.7.5 Neural Network Models for Discrete Choice . . . . 52
2.7.6 Models with Multinomial Ordered Choice . . . . . 53
2.8 The Black Box Criticism and Data Mining . . . . . . . . 55
2.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.9.1 MATLAB Program Notes . . . . . . . . . . . . . . 58
2.9.2 Suggested Exercises . . . . . . . . . . . . . . . . . 58
3 Estimation of a Network with Evolutionary Computation 59
3.1 Data Preprocessing . . . . . . . . . . . . . . . . . . . . . 59
3.1.1 Stationarity: Dickey-Fuller Test . . . . . . . . . . . 59
3.1.2 Seasonal Adjustment: Correction for Calendar
Effects . . . . . . . . . . . . . . . . . . . . . . . . 61
3.1.3 Data Scaling . . . . . . . . . . . . . . . . . . . . . 64
3.2 The Nonlinear Estimation Problem . . . . . . . . . . . . 65
3.2.1 Local Gradient-Based Search: The Quasi-Newton
Method and Backpropagation . . . . . . . . . . . 67
3.2.2 Stochastic Search: Simulated Annealing . . . . . . 70
3.2.3 Evolutionary Stochastic Search: The Genetic
Algorithm . . . . . . . . . . . . . . . . . . . . . . 72
3.2.4 Evolutionary Genetic Algorithms . . . . . . . . . . 75
3.2.5 Hybridization: Coupling Gradient-Descent,
Stochastic, and Genetic Search Methods . . . . . . 75
3.3 Repeated Estimation and Thick Models . . . . . . . . . . 77
3.4 MATLAB Examples: Numerical Optimization and
Network Performance . . . . . . . . . . . . . . . . . . . . 78
3.4.1 Numerical Optimization . . . . . . . . . . . . . . . 78
3.4.2 Approximation with Polynomials and
Neural Networks . . . . . . . . . . . . . . . . . . . 80
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.5.1 MATLAB Program Notes . . . . . . . . . . . . . . 83
3.5.2 Suggested Exercises . . . . . . . . . . . . . . . . . 84
4 Evaluation of Network Estimation 85
4.1 In-Sample Criteria . . . . . . . . . . . . . . . . . . . . . . 85
4.1.1 Goodness of Fit Measure . . . . . . . . . . . . . . 86
4.1.2 Hannan-Quinn Information Criterion . . . . . . . 86
4.1.3 Serial Independence: Ljung-Box and McLeod-Li
Tests . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.1.4 Symmetry . . . . . . . . . . . . . . . . . . . . . . 89
4.1.5 Normality . . . . . . . . . . . . . . . . . . . . . . 89
4.1.6 Neural Network Test for Neglected Nonlinearity:
Lee-White-Granger Test . . . . . . . . . . . . . . 90
4.1.7 Brock-Deckert-Scheinkman Test for Nonlinear
Patterns . . . . . . . . . . . . . . . . . . . . . . . 91
4.1.8 Summary of In-Sample Criteria . . . . . . . . . . . 93
4.1.9 MATLAB Example . . . . . . . . . . . . . . . . . 93
4.2 Out-of-Sample Criteria . . . . . . . . . . . . . . . . . . . 94
4.2.1 Recursive Methodology . . . . . . . . . . . . . . . 95
4.2.2 Root Mean Squared Error Statistic . . . . . . . . . 96
4.2.3 Diebold-Mariano Test for Out-of-Sample Errors . . 96
4.2.4 Harvey, Leybourne, and Newbold Size Correction
of Diebold-Mariano Test . . . . . . . . . . . . . . 97
4.2.5 Out-of-Sample Comparison with Nested Models . . 98
4.2.6 Success Ratio for Sign Predictions: Directional
Accuracy . . . . . . . . . . . . . . . . . . . . . . . 99
4.2.7 Predictive Stochastic Complexity . . . . . . . . . . 100
4.2.8 Cross-Validation and the .632 Bootstrapping
Method . . . . . . . . . . . . . . . . . . . . . . . . 101
4.2.9 Data Requirements: How Large for Predictive
Accuracy? . . . . . . . . . . . . . . . . . . . . . . 102
4.3 Interpretive Criteria and Significance of Results . . . . . . 104
4.3.1 Analytic Derivatives . . . . . . . . . . . . . . . . . 105
4.3.2 Finite Differences . . . . . . . . . . . . . . . . . . 106
4.3.3 Does It Matter? . . . . . . . . . . . . . . . . . . . 107
4.3.4 MATLAB Example: Analytic and Finite
Differences . . . . . . . . . . . . . . . . . . . . . . 107
4.3.5 Bootstrapping for Assessing Significance . . . . . . 108
4.4 Implementation Strategy . . . . . . . . . . . . . . . . . . 109
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.5.1 MATLAB Program Notes . . . . . . . . . . . . . . 110
4.5.2 Suggested Exercises . . . . . . . . . . . . . . . . . 111
II Applications and Examples 113
5 Estimating and Forecasting with Artificial Data 115
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.2 Stochastic Chaos Model . . . . . . . . . . . . . . . . . . . 117
5.2.1 In-Sample Performance . . . . . . . . . . . . . . . 118
5.2.2 Out-of-Sample Performance . . . . . . . . . . . . . 120
5.3 Stochastic Volatility/Jump Diffusion Model . . . . . . . . 122
5.3.1 In-Sample Performance . . . . . . . . . . . . . . . 123
5.3.2 Out-of-Sample Performance . . . . . . . . . . . . . 125
5.4 The Markov Regime Switching Model . . . . . . . . . . . 125
5.4.1 In-Sample Performance . . . . . . . . . . . . . . . 128
5.4.2 Out-of-Sample Performance . . . . . . . . . . . . . 130
5.5 Volatality Regime Switching Model . . . . . . . . . . . . 130
5.5.1 In-Sample Performance . . . . . . . . . . . . . . . 132
5.5.2 Out-of-Sample Performance . . . . . . . . . . . . . 132
5.6 Distorted Long-Memory Model . . . . . . . . . . . . . . . 135
5.6.1 In-Sample Performance . . . . . . . . . . . . . . . 136
5.6.2 Out-of-Sample Performance . . . . . . . . . . . . . 137
5.7 Black-Sholes Option Pricing Model: Implied Volatility
Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.7.1 In-Sample Performance . . . . . . . . . . . . . . . 140
5.7.2 Out-of-Sample Performance . . . . . . . . . . . . . 142
5.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.8.1 MATLAB Program Notes . . . . . . . . . . . . . . 142
5.8.2 Suggested Exercises . . . . . . . . . . . . . . . . . 143
6 Times Series: Examples from Industry and Finance 145
6.1 Forecasting Production in the Automotive Industry . . . 145
6.1.1 The Data . . . . . . . . . . . . . . . . . . . . . . . 146
6.1.2 Models of Quantity Adjustment . . . . . . . . . . 148
6.1.3 In-Sample Performance . . . . . . . . . . . . . . . 150
6.1.4 Out-of-Sample Performance . . . . . . . . . . . . . 151
6.1.5 Interpretation of Results . . . . . . . . . . . . . . 152
6.2 Corporate Bonds: Which Factors Determine the
Spreads? . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
6.2.1 The Data . . . . . . . . . . . . . . . . . . . . . . . 157
6.2.2 A Model for the Adjustment of Spreads . . . . . . 157
6.2.3 In-Sample Performance . . . . . . . . . . . . . . . 160
6.2.4 Out-of-Sample Performance . . . . . . . . . . . . . 160
6.2.5 Interpretation of Results . . . . . . . . . . . . . . 161
6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.3.1 MATLAB Program Notes . . . . . . . . . . . . . . 166
6.3.2 Suggested Exercises . . . . . . . . . . . . . . . . . 166
7 Inflation and Deflation: Hong Kong and Japan 167
7.1 Hong Kong . . . . . . . . . . . . . . . . . . . . . . . . . . 168
7.1.1 The Data . . . . . . . . . . . . . . . . . . . . . . . 169
7.1.2 Model Specification . . . . . . . . . . . . . . . . . 174
7.1.3 In-Sample Performance . . . . . . . . . . . . . . . 177
7.1.4 Out-of-Sample Performance . . . . . . . . . . . . . 177
7.1.5 Interpretation of Results . . . . . . . . . . . . . . 178
7.2 Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
7.2.1 The Data . . . . . . . . . . . . . . . . . . . . . . . 184
7.2.2 Model Specification . . . . . . . . . . . . . . . . . 189
7.2.3 In-Sample Performance . . . . . . . . . . . . . . . 189
7.2.4 Out-of-Sample Performance . . . . . . . . . . . . . 190
7.2.5 Interpretation of Results . . . . . . . . . . . . . . 191
7.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 196
7.3.1 MATLAB Program Notes . . . . . . . . . . . . . . 196
7.3.2 Suggested Exercises . . . . . . . . . . . . . . . . . 196
8 Classification: Credit Card Default and Bank Failures 199
8.1 Credit Card Risk . . . . . . . . . . . . . . . . . . . . . . 200
8.1.1 The Data . . . . . . . . . . . . . . . . . . . . . . . 200
8.1.2 In-Sample Performance . . . . . . . . . . . . . . . 200
8.1.3 Out-of-Sample Performance . . . . . . . . . . . . . 202
8.1.4 Interpretation of Results . . . . . . . . . . . . . . 203
8.2 Banking Intervention . . . . . . . . . . . . . . . . . . . . 204
8.2.1 The Data . . . . . . . . . . . . . . . . . . . . . . . 204
8.2.2 In-Sample Performance . . . . . . . . . . . . . . . 205
8.2.3 Out-of-Sample Performance . . . . . . . . . . . . . 207
8.2.4 Interpretation of Results . . . . . . . . . . . . . . 208
8.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 209
8.3.1 MATLAB Program Notes . . . . . . . . . . . . . . 210
8.3.2 Suggested Exercises . . . . . . . . . . . . . . . . . 210
9 Dimensionality Reduction and Implied Volatility
Forecasting 211
9.1 Hong Kong . . . . . . . . . . . . . . . . . . . . . . . . . . 212
9.1.1 The Data . . . . . . . . . . . . . . . . . . . . . . . 212
9.1.2 In-Sample Performance . . . . . . . . . . . . . . . 213
9.1.3 Out-of-Sample Performance . . . . . . . . . . . . . 214
9.2 United States . . . . . . . . . . . . . . . . . . . . . . . . 216
9.2.1 The Data . . . . . . . . . . . . . . . . . . . . . . . 216
9.2.2 In-Sample Performance . . . . . . . . . . . . . . . 216
9.2.3 Out-of-Sample Performance . . . . . . . . . . . . . 218
9.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 219
9.3.1 MATLAB Program Notes . . . . . . . . . . . . . . 220
9.3.2 Suggested Exercises . . . . . . . . . . . . . . . . . 220
Bibliography 221
Index 233

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