We study residual control charts for the detection of sudden changes in time series with an underlying time-varying trend. Our control charts compare the most recent observations to their direct predecessors by applying two-sample tests in a moving time window to one-step-ahead prediction errors obtained from a local linear regression. Global model assumptions, a fixed target value, or large sets of historical in-control data are unnecessary therefore. Disturbing in-control structures, like short outlier patches or minor fluctuations, are resisted by using robust methods. Our simulation results indicate that a control chart based on the two-sample Hodges-Lehmann estimator in combination with repeated-median regression possesses an approximately distribution-free in-control average run length, good robustness against outliers, and a desirable detection quality.

中文翻译：

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局部线性时间序列均值的稳健控制图

我们研究残差控制图，用于检测具有潜在时变趋势的时间序列的突然变化。我们的控制图通过将移动时间窗口中的两个样本测试应用于从局部线性回归获得的提前一步预测误差，将最新的观察结果与其直接前辈进行比较。因此，不需要全局模型假设、固定目标值或大量历史控制数据集。使用稳健的方法可以抵抗干扰的控制结构，例如短的异常值补丁或微小的波动。我们的模拟结果表明，基于双样本 Hodges-Lehmann 估计量与重复中值回归相结合的控制图具有近似无分布的控制平均运行长度，对异常值具有良好的鲁棒性，