An Invariance Property of the Common Trends Under Linear Transformations of the Data

15 Pages Posted: 1 Nov 2010

See all articles by Soren Johansen

Soren Johansen

University of Copenhagen - Department of Economics; Aarhus University - CREATES

Katarina Juselius

University of Copenhagen - Department of Economics

Date Written: October 31, 2010

Abstract

It is well known that if X(t) is a nonstationary process and Y(t) is a linear function of X(t), then cointegration of Y(t) implies cointegration of X(t). We want to find an analogous result for common trends if X(t) is generated by a finite order VAR. We first show that Y(t) has an infinite order VAR representation in terms of its prediction errors, which are a linear process in the prediction error for X(t). We then apply this result to show that the limit of the common trends for Y(t) are linear functions of the common trends for X(t). We illustrate the findings with a small analysis of the term structure of interest rates.

Keywords: Cointegration Vectors, Common Trends, Prediction Errors

JEL Classification: C32

Suggested Citation

Johansen, Soren and Juselius, Katarina, An Invariance Property of the Common Trends Under Linear Transformations of the Data (October 31, 2010). University of Copenhagen Department of Economics Discussion Paper No. 10-30, Available at SSRN: https://ssrn.com/abstract=1701167 or http://dx.doi.org/10.2139/ssrn.1701167

Soren Johansen (Contact Author)

University of Copenhagen - Department of Economics ( email )

Øster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Aarhus University - CREATES ( email )

Nordre Ringgade 1
Aarhus, DK-8000
Denmark

Katarina Juselius

University of Copenhagen - Department of Economics ( email )

Øster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

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