Bernt P. Stigum
- Published in print:
- 2014
- Published Online:
- September 2015
- ISBN:
- 9780262028585
- eISBN:
- 9780262323109
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262028585.003.0006
- Subject:
- Economics and Finance, Econometrics
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 ...
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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.Less
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.
