Lin, Yan-Xia; McCrae, Michael The effects of \(I(1)\) series on cointegration inference. (English) Zbl 1035.62093 J. Appl. Math. Decis. Sci. 6, No. 4, 229-240 (2002). Summary: 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 \(\xi'X_t\) for a certain vector \(\xi\) in the period \(0<t\leq T_1\). 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. 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 \(t\leq T_1\). MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:cointegration; cointegrating vector; ARIMA model; eigenvalues; simulations PDFBibTeX XMLCite \textit{Y.-X. Lin} and \textit{M. McCrae}, J. Appl. Math. Decis. Sci. 6, No. 4, 229--240 (2002; Zbl 1035.62093) Full Text: DOI EuDML