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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 with i.i.d. (0,Ω_{x}) errors ε_{xt}. We first show that Y_{t} has an infinite order VAR representation in terms of its white noise prediction errors, ε_{yt}, which are a linear process in ε_{xt}, the prediction error for X_{t}. We then apply this result to show that the limit of the common trends for Y_{t} generated by ε_{yt}, are linear functions of the common trends for X_{t}, generated by ε_{xt}.
We illustrate the findings with a small analysis of the term structure of interest rates.
We illustrate the findings with a small analysis of the term structure of interest rates.
Original language  English 

Journal  Journal of Econometrics 
Volume  178 
Issue number  Part 2 
Pages (fromto)  310315 
Number of pages  6 
ISSN  03044076 
DOIs  
Publication status  Published  2014 
Bibliographical note
JEL classification: C32Activities
 1 Lecture and oral contribution

An asymptotic invariance property of the common trends under linear transformations of the data
Søren Johansen (Lecturer)
22 Oct 2013Activity: Talk or presentation types › Lecture and oral contribution