An invariance property of the common trends under linear transformations of the data
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.
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- 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 (IfW), vol. 2, 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 (IfW).
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