1 Introduction |
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1 | (6) |
2 Economic Systems With Expectations Feedback |
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7 | (16) |
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2.1 An Introductory Example |
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8 | (2) |
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10 | (2) |
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2.3 Forecasting Rules With Finite Memory |
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12 | (2) |
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2.4 Consistent Forecasting Rules |
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14 | (3) |
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2.5 Unbiased Forecasting Rules |
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17 | (6) |
3 Adaptive Learning in Linear Models |
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23 | (34) |
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24 | (4) |
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3.2 Unbiased Forecasting Rules |
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28 | (9) |
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30 | (4) |
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3.2.2 Linear MSV Predictors |
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34 | (3) |
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3.3 Approximating Unbiased Forecasting Rules |
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37 | (2) |
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3.4 Convergence of an AML-Based Learning Scheme |
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39 | (6) |
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3.5 Mathematical Appendix |
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45 | (12) |
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3.5.1 On the Stability of Linear Systems |
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45 | (2) |
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3.5.2 Proofs of Theorem 3.2 and Theorem 3.3 |
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47 | (10) |
4 Economic Models Subject to Stationary Noise |
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57 | (28) |
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4.1 Forecasting Rules for Stationary Noise |
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59 | (9) |
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4.1.1 Consistent Forecasting Rules |
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61 | (3) |
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4.1.2 Unbiased Forecasting Rules |
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64 | (4) |
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4.2 Existence of Unbiased Forecasting Rules |
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68 | (5) |
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73 | (2) |
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75 | (4) |
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4.5 Mathematical Appendix |
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79 | (6) |
5 Nonparametric Adaptive Learning |
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85 | (42) |
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5.1 The Method of Stochastic Approximation |
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86 | (4) |
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5.2 A Basic Convergence Result |
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90 | (9) |
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5.3 Some Probabilistic Prerequisites |
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99 | (3) |
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5.4 Sufficient Conditions for Contractions |
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102 | (6) |
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5.5 Mathematical Appendix |
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108 | (19) |
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5.5.1 Sobolev Imbedding Theorem |
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108 | (3) |
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5.5.2 Proofs of Section 5.2 |
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111 | (7) |
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5.5.3 Proofs of Section 5.4 |
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118 | (9) |
6 Stochastic Exchange Economies |
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127 | (12) |
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6.1 A Model of Pure Exchange |
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127 | (2) |
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6.2 The Existence of Perfect Forecasting Rules |
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129 | (2) |
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6.3 Perfect Foresight Dynamics |
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131 | (3) |
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6.4 Adaptive Learning of Perfect Forecasting Rules |
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134 | (2) |
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6.5 Mathematical Appendix |
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136 | (3) |
7 Heterogeneous Beliefs in a Financial Market |
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139 | (32) |
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141 | (4) |
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7.2 Heterogeneous Beliefs |
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145 | (2) |
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7.3 Risk Premia and Reference Portfolios |
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147 | (2) |
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7.4 Mean-Variance Preferences |
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149 | (3) |
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7.5 Perfect Forecasting Rules |
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152 | (4) |
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7.5.1 Perfect Forecasting Rules for First Moments |
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152 | (1) |
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7.5.2 Perfect Forecasting Rules for Second Moments |
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153 | (3) |
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7.6 Dynamics Under Rational Expectations |
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156 | (5) |
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7.7 Adaptive Learning With Heterogeneous Beliefs |
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161 | (7) |
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161 | (1) |
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7.7.2 The Case With Two Mediators |
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162 | (6) |
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7.8 Mathematical Appendix |
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168 | (3) |
References |
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171 | |