An Asymptotic Invariance Property of Common Trends under Linear Transformations of the Data

TY - JOUR

T1 - An Asymptotic Invariance Property of Common Trends under Linear Transformations of the Data

AU - Johansen, Søren

AU - Juselius, Katarina

N1 - JEL classification: C32

PY - 2014/1

Y1 - 2014/1

N2 - 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.

AB - 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.

U2 - 10.1016/j.jeconom.2013.08.029

DO - 10.1016/j.jeconom.2013.08.029

M3 - Journal article

SN - 0304-4076

VL - 178

SP - 310

EP - 315

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - Part 2

ER -