Department of Economics and Business Economics

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

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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. We illustrate the findings with a small analysis of the term structure of interest rates.

Original languageEnglish
JournalJournal of Econometrics
Volume178
IssuePart 2
Pages (from-to)310-315
Number of pages6
ISSN0304-4076
DOIs
Publication statusPublished - 1 Jan 2014

    Research areas

  • Cointegration vectors, Common trends, Prediction errors

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