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An asymptotic invariance property of the common trends under linear transformations of the data

Soren Johansen () and Katarina Juselius

Journal of Econometrics, 2014, vol. 178, issue P2, pages 310-315

Abstract: It is well known that if Xt is a nonstationary process and Yt is a linear function of Xt, then cointegration of Yt implies cointegration of Xt. We want to find an analogous result for common trends if Xt is generated by a finite order VAR with i.i.d. (0,Ωx) errors εxt. We first show that Yt has an infinite order VAR representation in terms of its white noise prediction errors, εyt, which are a linear process in εxt, the prediction error for Xt. We then apply this result to show that the limit of the common trends for Yt generated by εyt, are linear functions of the common trends for Xt, generated by εxt.

Keywords: Cointegration vectors; Common trends; Prediction errors (search for similar items in EconPapers)
JEL-codes: C32 (search for similar items in EconPapers)
Date: 2014
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Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

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