System-Theoretic Methods in Economic Modelling I (eBook)

Front Cover 1
System-Theoretic Methods in Economic Modelling I 4
Copyright Page 5
Table of Contents 6
PREFACE 8
CHAPTER 1. A TWO-STEP STATE SPACE TIME SERIES MODELING METHOD 10
1. INTRODUCTION 10
2. DYNAMIC AGGREGATION 11
3. MODELING PROCEDURE 12
4. DECOMPOSITION INTO TRENDS AND CYCLICAL COMPONENTS 14
5. EXAMPLES 16
6. CONCLUDING REMARKS 19
REFERENCES 20
APPENDIX 20
CHAPTER 2. SYSTEM THEORETIC TIME SERIES: AN APPLICATIONTO INVENTORIES AND PRICES OF CALIFORNIA RANGE CATTLE 22
1. INTRODUCTION 22
2. SYSTEM THE ORETIC TIME SERIES (STTS): A BRIEF OVER VIEW OF THE PROCEDURE 23
3. THE BEEF MODEL 27
4. CONCLUSION 32
REFERENCES 32
CHAPTER 3. MULTIVARIATE TIME SERIES ANALYSIS WITHSTATE SPACE MODELS 34
1. INTRODUCTION 34
2. ESTIMATION OF SYSTEM MATRICES FOR AUTOREGRESSIVE PROCESSES 35
3. AUTOREGRESSIVE PROCESSES WITH EXOGENOUS VARIABLES 39
4. EXTENSION TO AUTOREGRESSIVE MOVING AVERAGE PROCESSES 41
5. CONCLUDING REMARKS 45
REFERENCES 45
CHAPTER 4. OPTIMAL FORECASTING OF DISCRETE STOCK AND FLOW DATA GENERATED BY A HIGHER ORDER CONTINUOUS TIME SYSTEM 48
1. INTRODUCTION 48
2. THE MODEL AND ITS ESTIMATION 50
3. AN OPTIMAL FORECASTING ALGORITHM 54
4 . THE TREATMENT OF EXOGENOUS VARIABLES 57
5. CONCLUSION 58
REFERENCES 58
CHAPTER 5. TIME-VARYING LINEAR REGRESSION VIA FLEXIBLE LEAST SQUARES 60
1. INTRODUCTION 60
2. TIME - VARYING LINEAR REGRESSION PROBLEM 63
3. FLEXIBLE LEAST SQUARES (FLS) 63
4. THE FLS SOLUTION: MATRIX REPRESENTATION 66
5. EXACT SEQUENTIAL DERIVATION OF THE FLS SOLUTION 67
6. FLS AND OLS : A GEOMETRIC COMPARISON 70
7. REGIME SHIFT: AROBUSTNESS STUDY FOR FLS 71
8. SIMULATION AND EMPIRICAL STUDIES 73
9. TOPICS FOR FUTURE RESEARCH 76
REFERENCES 77
APPENDIX A 78
APPENDIX B 82
CHAPTER 6. NONSTATIONARY TIME SERIES IDENTIFICATION 92
1. INTRODUCTION 92
2. PARAMETER ESTIMATION FOR CONTROLLED TIME SERIES 93
3. ORDER ESTIMATION FOR CONTROLLED TIME SERIES 97
4. RELAXATION OF SPR CONDITION 99
5. IDENTIFICATION OF A CLASS OF NONSTATIONARY ARMA PROCESSES 100
6. CONCLUSION 102
REFERENCES 102
CHAPTER 7. THE CODING THEOREM AND ORDINARY LEAST-SQUARES MODELS IN ECONOMICS 104
1. INTRODUCTION 104
2. THE OLS CHANNEL WITH FEEDBACK 104
3. OPTIMAL OLS CODES 105
4. MARKET APPLICATIONS 106
5. SUMMARY 109
REFERENCES 109
CHAPTER 8. THE INFORMATION TABLEAU OF A LINEAR ALLOCATION MODEL 110
1. INTRODUCTION 110
2. THE UNIVARIATE LINEAR REGRESSION MODEL 110
3. A MULTIVARIATE EXTENSION 111
4. THE INFORMATION TABLEAU OF A LINEARDEM AND MODEL 111
REFERENCES 113
CHAPTER 9. THE PREJUDICES OF LEAST SQUARES, PRINCIPAL COMPONENTS AND COMMON FACTORS SCHEMES 114
1. INTRODUCTION 114
2. LEAST SQUARES SCHEME 115
3. PRINCIPAL COMPONENTS SCHEME 121
4. COMMON FACTOR SCHEME 123
5. CONCLUDINGRE MARKS 127
REFERENCES 127
CHAPTER 10. IDENTIFICATION OF A LINEAR SYSTEM FROM INEXACT DATA: A THREE-VARIABLE EXAMPLE 130
1. INTRODUCTION 130
2. GENERAL LINEAR SYSTEM IDENTIFICATION 131
3. LEAST SQUARES SCHEMES 134
4. FRISCH AND STATISTICAL COMMON FACTOR SCHEMES 139
5. A COMPARISON OF THE SOLUTIONS 143
6. CONCLUDING REMARKS 145
REFERENCES 145
APPENDIX A 146
APPENDIX B 147
CHAPTER 11. A SUPERLINEARLY CONVERGENT CONSTRAINED MIN-MAX ALGORITHM FOR RIVAL MODELS OF THE SAME SYSTEM 150
1. INTRODUCTION 150
2. THE MIN - MAX PROBLEM AND A SADDLE POINT SOLUTION 153
3. THE ALGORITHM 155
4. GLOBAL CONVERGENCE 157
5. CONVERGENCE TO UNIT STEP SIZES AND THE SUPER LINEAR CONVERGENCE RATE OF THE ALGORITHM 159
REFERENCES 161
CHAPTER 12. COST-BENEFIT ANALYSIS WITH SWITCHING REGIMES:AN APPLICATION OF THE THEORY OF PLANNING 162
1. INTRODUCTION : PLANNING, SWITCHING REGIMES AND COST-BENEFIT ANALYSIS 162
2. THE FRAME WORK FOR THE PLANNING PROBLEM 163
3. OPTIMAL SWITCHING REGIME : THE CASE OF CERTAINTY 165
4. OPTIMAL SWITCHING REGIME: THE CASE OF UNCERTAINTY 168
5. AN EXAMPLE OF SWITCHES UNDER UNCERTAINTY 170
6. OPTIMALSWIT CHINGRE GIME: THE CASE OF LEARNING FROM EXPERIENCE 171
7. CONCLUSIONS 171
REFERENCES 172
CHAPTER 13. AN INTEGRATED SYSTEM MODEL FOR A FISHERY MANAGEMENT PROCESS—I 174
1. INTRODUCTION 174
2. THE ROLE OF MODELING IN THE FISHERY MANAGEMENT DECISION PROCESS 175
3. MODULES OF FISYS 176
4. INTEGRATING FRAMEWORK VIA PARTIAL EQUILIBRIUM 181
5. THE USE OF FISYS IN A FISHERY MANAGEMENT DECISION PROCESS 185
6. CONCLUDING REMARKS 187
REFERENCES 188
CHAPTER 14. A LATTICE-THEORETIC APPROACH TO A CLASS OF DYNAMIC GAMES 190
1. INTRODUCTION AND PROBLEM STATEMENT 190
2. MATHEMATICAL BACKGROUND 191
3. PROOFS 192
REFERENCES 194