Department of Economics and Business Economics

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

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An asymptotic invariance property of the common trends under linear transformations of the data. / Johansen, Søren; Juselius, Katarina.

In: Journal of Econometrics, Vol. 178, No. Part 2, 01.01.2014, p. 310-315.

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Johansen, Søren ; Juselius, Katarina. / An asymptotic invariance property of the common trends under linear transformations of the data. In: Journal of Econometrics. 2014 ; Vol. 178, No. Part 2. pp. 310-315.

Bibtex

@article{60a6548641d4498f844dcd2d136e0eea,
title = "An asymptotic invariance property of the common trends under linear transformations of the data",
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. We illustrate the findings with a small analysis of the term structure of interest rates.",
keywords = "Cointegration vectors, Common trends, Prediction errors",
author = "S{\o}ren Johansen and Katarina Juselius",
year = "2014",
month = "1",
day = "1",
doi = "10.1016/j.jeconom.2013.08.029",
language = "English",
volume = "178",
pages = "310--315",
journal = "Journal of Econometrics",
issn = "0304-4076",
publisher = "Elsevier BV",
number = "Part 2",

}

RIS

TY - JOUR

T1 - An asymptotic invariance property of the common trends under linear transformations of the data

AU - Johansen, Søren

AU - Juselius, Katarina

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

KW - Cointegration vectors

KW - Common trends

KW - Prediction errors

U2 - 10.1016/j.jeconom.2013.08.029

DO - 10.1016/j.jeconom.2013.08.029

M3 - Journal article

AN - SCOPUS:84889085527

VL - 178

SP - 310

EP - 315

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - Part 2

ER -