The effects of I(1) series on cointegration inference

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 ξ′Xt for certain vector ξ 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) for t ≤ T1.