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Econometrics in a Formal Science of EconomicsTheory and the Measurement of Economic Relations$
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Bernt P. Stigum

Print publication date: 2014

Print ISBN-13: 9780262028585

Published to MIT Press Scholarship Online: September 2015

DOI: 10.7551/mitpress/9780262028585.001.0001

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Non-Linear Cointegration in Foreign Exchange

Non-Linear Cointegration in Foreign Exchange

(p.233) 8 Non-Linear Cointegration in Foreign Exchange
Econometrics in a Formal Science of Economics

Bernt P. Stigum

The MIT Press

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.

Keywords:   integrated processes, linear cointegration, non-linear cointegration, non-linear polynomial cointegration, empirical relevance, foreign exchange, test statistics, economic theory, theory-data confrontation, second-order random processes

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