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

TY - UNPB

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

AU - Johansen, Søren

AU - Juselius, Katarina

N1 - JEL classification: C32

PY - 2010

Y1 - 2010

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. We first show that Y(t) has an infinite order VAR representation in terms of its prediction errors, which are a linear process in the prediction error for X(t). We then apply this result to show that the limit of the common trends for Y(t) are linear functions of the common trends for X(t). 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. We first show that Y(t) has an infinite order VAR representation in terms of its prediction errors, which are a linear process in the prediction error for X(t). We then apply this result to show that the limit of the common trends for Y(t) are linear functions of the common trends for X(t). We illustrate the findings with a small analysis of the term structure of interest rates.

M3 - Working paper

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

PB - Department of Economics, University of Copenhagen

ER -