Abstract
We develop a CUSUM-type monitoring procedure based on the ordinary least squares residuals for detecting structural changes in models with a trend. A proper boundary function is designed to control the size. We derive the limiting null distribution and the consistency of the procedure under the alternative. In addition, we derive the asymptotic distribution of the delay time for the CUSUM procedure as well as the fluctuation procedure proposed by Qi etal. (2016). The simulation and empirical results indicate that although neither procedure is uniformly superior to the other, the CUSUM test is more suitable for an early break.
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