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PARTI UNIT-ROOT TESTS IN UNIVARIATE ANALYSIS 1
1. Stochastic Trend and Overview of Part I 3
1.1 Stochastic Trend 3
1.2 Stochastic Trend as a Logical Implication of an
Economic Theory? 9
1.3 Influences upon the Testing of Economic Theories 10
1.4 Overview of Part I 13
2. Trend Stationarity vs. Difference Stationarity 16
2.1 Basic Discrimination 16
2.2 Long-Run Component 17
2.3 Dominating Root of Characteristic Polynomial 22
2.4 Non-Separate Hypotheses 24
2.5 Time Aggregation and Other Remarks on the Data 25
3. Discrimination in Terms of the Long-Run Component:
A Test for Trend Stationarity 28
3.1 Non-parametric Variance Ratios and Mean-Reverting 28
3.2 Difficulty of Discrimination through the Non-parametric
Variance Ratios 30
3.3 Time-Series Decomposition 33
3.4 Parametric MA Unit-Root Test: A Test for Trend
Stationarity against Difference Stationarity 34
4. Unit-Root Asymptotic Theories (I) 40
4.1 Pure Random Walk without a Drift 40
4.2 Pure Random Walk possibly with a Drift 44
PART II CO-INTEGRATION ANALYSIS IN ECONOMETRICS 115
Overview 117
11. Different Modelling Strategies on Multiple Relationships 120
11.1 Economic Models and Statistical Models 120
77.2 Weak Exogeneity 124
11.3 Granger Non-Causality 129
12. Conceptual Framework of the Co-Integration and its
Relation to Economic Theories 135
72.7 Co-integration in the MA Representation 136
72.2 Granger Representation Theorem 140
12.3 Economic Theory and Co-integration 150
Highlights of Chapter 12 161
13. Asymptotic Inference Theories on Co-Integrated Regressions 164
13.7 Pure Random Walk 166
73.2 Deterministic Polynomial Trends 178
13.3 Serially Correlated Case 187
13.4 Miscellaneous Remarks including Direction of Co-integration 193
13.5 A Priori Specified Co-integrating Vector 198
13.6 Shortcomings in Many Past Empirical Studies 199
Highlights of Chapter 13
14. Inference on Dynamic Econometric Models 204
14.1 Hendry Model with the Two-Step Method 207
14.2 Dynamic Equation with the Two-Step Method 209
14.3 Hendry Model with the Single-Step Method 211
14.4 Dynamic Equation with the Single-Step Method 215
15. Maximum-Likelihood Inference Theory of Co-Integrated VAR 219
75.7 Determination of Co-integration Rank 221
75.2 Testing for Restrictions on the Co-integration Space 230
75.3 A Common Practice on B' 236
75.4 Weak Exogeneity and Granger Non-causality 236
75.5 Applications 241
Appendix 1 Spectral Analysis 247
Appendix 2 Wiener (Brownian Motion) Process 249
Appendix 3 Asymptotic Theories involving a Linear Deterministic
Trend 251
Appendix 4 OLS Estimator of Difference-Stationary Autoregressive
Process 258
Appendix 5 Mathematics for the VAR, VMA, and VARMA 260
Appendix 6 Fully Modified Least-Squares Estimator 265
References 269
Subject Index 289
Author Index 291
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