The article discusses a method to test time series data for a unit root while considering the possibility of a break in the trend. The researchers developed a break fraction estimator that accurately identifies trend breaks in the presence of a unit root or near-unit root. This estimator also works well when there is no break in trend, converging to zero effectively. By incorporating this estimator into a unit root test, the researchers were able to apply critical values accurately, even when there is no trend break. They also proposed a pre-test for trend breaks to further improve the testing procedure.