Journal of Applied Mathematics and Decision Sciences 
Volume 6 (2002), Issue 4, Pages 229-240
doi:10.1155/S1173912602000160

The effects of I(1) series on cointegration inference

Yan-Xia Lin1 and Michael Mccrae2

 1School of Mathematics and Applied Statistics, University of Wollongong, Wollongong 2522, NSW , Australia
2Department of Accounting and Finance, University of Wollongong, Wollongong 2522, NSW, Australia

Abstract

Under traditional cointegration tests, some eligible I(1) time series systems Xt, that are not cointegrated over a given time period, say (0,T1], sometimes test as cointegrated over sub-periods. That is, the system appears to have a stationary linear structure ζ′Xt for certain vector ζ in the period 0<t≤T1. Understanding the dynamics between cointegration test power and restricted sample size that causes this inversion of results is a crucial issue when forecasting over extended future time periods. In this paper, we consider non-cointegrated systems that are closely related to collinear systems. We apply a residual based procedure to such systems and establish a criterion for making the decision whether or not Xt can be continuously accepted as I(0) for t>T1 when Xt was accepted as I(0) fort≤T1.