• ARMA series;
  • Brownian bridge;
  • changepoints;
  • CUSUM;
  • likelihood ratio
  • C22

Several tests for detecting mean shifts at an unknown time in stationary time series have been proposed, including cumulative sum (CUSUM), Gaussian likelihood ratio (LR), maximum of F(Fmax) and extreme value statistics. This article reviews these tests, connects them with theoretical results, and compares their finite sample performance via simulation. We propose an adjusted CUSUM statistic which is closely related to the LR test and which links all tests. We find that tests based on CUSUMing estimated one-step-ahead prediction residuals from a fitted autoregressive moving average perform well in general and that the LR and Fmax tests (which induce substantial computational complexities) offer only a slight increase in power over the adjusted CUSUM test. We also conclude that CUSUM procedures work slightly better when the changepoint time is located near the centre of the data, but the adjusted CUSUM methods are preferable when the changepoint lies closer to the beginning or end of the data record. Finally, an application is presented to demonstrate the importance of the choice of method.