Under traditional cointegration tests, some eligible I ( 1 ) time series systems X t , that are not cointegrated over a given time period, say ( 0 , T 1 ] , sometimes test as cointegrated over sub-periods. That is, the system appears to have a stationary linear structure ζ ′ X t for certain vector ζ in the period 0 < t ≤ T 1 . 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 X t can be continuously accepted as I ( 0 ) for t > T 1 when X t was accepted as I ( 0 ) for t ≤ T 1 .