
Contents
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8.1 Linearly and Non-Linearly Cointegrated Second-Order Random Processes 8.1 Linearly and Non-Linearly Cointegrated Second-Order Random Processes
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8.1.1 A Reformulation of I(k), k = 0, 1, 2, for Second-Order Random Processes 8.1.1 A Reformulation of I(k), k = 0, 1, 2, for Second-Order Random Processes
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8.1.2 Linear and Non-Linear Cointegration in Triples of Second-Order Random Processes 8.1.2 Linear and Non-Linear Cointegration in Triples of Second-Order Random Processes
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Linear cointegration Linear cointegration
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DEF8.2 DEF8.2
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Non-linear cointegration Non-linear cointegration
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Non-linear polynomial cointegration Non-linear polynomial cointegration
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8.2 A Formal Theory-Data Confrontation in Foreign Exchange 8.2 A Formal Theory-Data Confrontation in Foreign Exchange
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8.2.1 The Theory Universe 8.2.1 The Theory Universe
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8.2.2 Linear and Non-Linear Cointegration in the Theory Universe 8.2.2 Linear and Non-Linear Cointegration in the Theory Universe
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8.2.3 The Data Universe 8.2.3 The Data Universe
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8.2.4 The Bridge 8.2.4 The Bridge
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8.2.5 The MPD 8.2.5 The MPD
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8.3 Harald Goldstein’s Econometric AnalysisClose 8.3 Harald Goldstein’s Econometric AnalysisClose
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8.3.1 The Prescriptions That Underlie the Statistical Analysis 8.3.1 The Prescriptions That Underlie the Statistical Analysis
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8.3.2 Estimates of the Parameters of the MPD 8.3.2 Estimates of the Parameters of the MPD
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8.3.3 Remarks Concerning the Statistical Assumptions Underlying the Empirical Analysis 8.3.3 Remarks Concerning the Statistical Assumptions Underlying the Empirical Analysis
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8.3.4 Data-Admissible Models of the Data Universe and the MPD 8.3.4 Data-Admissible Models of the Data Universe and the MPD
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A 95-percent-confidence region for data-admissible models of the MPD A 95-percent-confidence region for data-admissible models of the MPD
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Interesting Ideas about the Structure of D Interesting Ideas about the Structure of D
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8.3.5 The Empirical Relevance of A1–A8 8.3.5 The Empirical Relevance of A1–A8
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8.3.6 Spot Prices in Foreign Exchange 8.3.6 Spot Prices in Foreign Exchange
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8.3.7 Concluding Remarks 8.3.7 Concluding Remarks
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8.4 André Anundsen’s Econometric Analysis 8.4 André Anundsen’s Econometric Analysis
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8.4.1 Vector-Autoregression-Based Results for Exchange-Rate Cointegration 8.4.1 Vector-Autoregression-Based Results for Exchange-Rate Cointegration
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8.4.2 Cointegration Analysis 8.4.2 Cointegration Analysis
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8.4.3 Testing for the Number of Cointegrating Relationships 8.4.3 Testing for the Number of Cointegrating Relationships
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8.4.4 Cross-Checks 8.4.4 Cross-Checks
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8.4.5 Concluding Remarks 8.4.5 Concluding Remarks
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8 Non-Linear Cointegration in Foreign Exchange
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Published:December 2014
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Abstract
Chapter VIII presents a novel mathematical theory of non-linear cointegration among second-order random processes. It begins by explaining why the accepted characterization of integrated second-order processes is inadequate for the analysis of non-linearly cointegrated economic systems, proposes alternative characterization of integrated processes, and develops novel ideas of non-linearly cointegrated second-order random processes. Thereafter, it presents a data confrontation of an economic theory about the dynamics of spot rates in foreign exchange whose variables share the behavior characteristics of the random processes in the mathematical theory. The data consist of weekly observations of a triple of exchange rates, and the empirical analysis is carried out in two ways – one by the methods of formal econometrics and another by the methods of present-day econometrics. The results of the two empirical analyses differ in interesting ways. Both agree that the behavior of the three exchange rates has the characteristics on which the mathematical theory insists, but their description of the dynamics of foreign exchange differ. Also, the present-day econometrics analysis rejects the empirical relevance of the given economic theory while the formal econometrics analysis accepts it. The acceptance of the theory carries interesting information about the dynamics of foreign exchange in social reality.
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