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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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Theory-Data Confrontations with Time-Series Data

Theory-Data Confrontations with Time-Series Data

(p.169) 6 Theory-Data Confrontations with Time-Series Data
Econometrics in a Formal Science of Economics

Bernt P. Stigum

The MIT Press

Chapter VI begins with a discussion of the axioms of a formal theory-data confrontation in which the data appear as vector-valued sequences of observations of a vector-valued random process. Then it describes important characteristics of I(1) ARIMA processes, one of which is their tendency to display long positive and negative sojourns. This property of the process can be used to carry out meaningful empirical analyses of positively valued time series; e.g., spot and forward exchange rate: Let the observations of the exchange rates be observations of an auxiliary I(1) ARIMA process, analyse them with currently available software programs, and check if long sequences of the exchange rates have the characteristics of an I(1) ARIMA process. A second characteristic of an I(1) ARIMA process is that any multivariate version of such a process can be written as an error correction model. In present-day econometrics, statistical analyses of error correction models of vector-valued time series are used to determine the degree of cointegration of the time series. The import of such an analysis hinges on the theoretical meaningfulness of the pertinent error correction model. The chapter demonstrates that an empirically relevant error correction model need not be theoretically meaningful.

Keywords:   theory-data confrontation, time series, I(1) ARIMA processes, long positive sojourns, positively valued time series, auxiliary variables, error-correction models, cointegrated time series, confluent relations, structural break in time-series

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