We show that the conventional CUSUM test for structural change can be applied to cointegrating regression residuals leading to a consistent residual based test for the null hypothesis of cointegration. The proposed tests are semiparametric and utilize fully modiﬁed residuals to correct for endogeneity and serial correlation and to scale out nuisance parameters. The limit distribution of the test is derived under both the null and the alternative hypothesis. The tests are easy to use and are found to perform quite well in a Monte Carlo experiment.
Xiao, Zhijie and Phillips, Peter C.B., "A CUSUM Test for Cointegration Using Regression Residuals" (2001). Cowles Foundation Discussion Papers. 1591.