We study online changepoint detection in the context of a linear regression model. We propose a class of heavily weighted statistics based on the CUSUM process of the regression residuals, which are specifically designed to ensure timely detection of breaks occurring early on during the monitoring horizon. We subsequently propose a class of composite statistics, constructed using different weighing schemes; the decision rule to mark a changepoint is based on the largest statistic across the various weights, thus effectively working like a veto-based voting mechanism, which ensures fast detection irrespective of the location of the changepoint. Our theory is derived under a very general form of weak dependence, thus being able to apply our tests to virtually all time series encountered in economics, medicine, and other applied sciences. Monte Carlo simulations show that our methodologies are able to control the procedure-wise Type I Error, and have short detection delays in the presence of breaks.

翻译：我们在线性回归模型背景下研究在线变化点检测问题。基于回归残差的CUSUM过程，我们提出了一类加权统计量，这些统计量经过专门设计，以确保在监测期内早期发生的断点能被及时检测。随后，我们提出了一类复合统计量，通过不同的加权方案构建；标记变化点的决策规则基于各权重下最大统计量值，从而有效实现类似否决投票机制，确保无论变化点位于何处都能快速检测。我们的理论推导基于极一般的弱依赖形式，因此能够将检验方法应用于经济学、医学及其他应用科学中几乎所有的时序数据。蒙特卡洛模拟表明，我们的方法能有效控制程序级第一类错误，并在存在断点的情况下实现较短的检测延迟。