An Invariance Property of the Common Trends under Linear Transformations of the Data
AbstractIt 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.
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Bibliographic InfoPaper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 10-30.
Length: 13 pages
Date of creation: Oct 2010
Date of revision:
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cointegration vectors; common trends; prediction errors;
Other versions of this item:
- Søren Johansen & Katarina Juselius, 2010. "An invariance property of the common trends under linear transformations of the data," CREATES Research Papers 2010-72, School of Economics and Management, University of Aarhus.
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-11-13 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Giese, Julia V., 2008.
"Level, Slope, Curvature: Characterising the Yield Curve in a Cointegrated VAR Model,"
Economics - The Open-Access, Open-Assessment E-Journal,
Kiel Institute for the World Economy, vol. 2(28), pages 1-20.
- Giese, Julia V., 2008. "Level, Slope, Curvature: Characterising the Yield Curve in a Cointegrated VAR Model," Economics Discussion Papers 2008-13, Kiel Institute for the World Economy.
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