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Journal of Applied Mathematics and Decision Sciences
Volume 6 (2002), Issue 4, Pages 229-240

The effects of I(1) series on cointegration inference

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

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 ζXt for certain vector ζ in the period 0<tT1. 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) fortT1.