This article proposes an online bootstrap scheme for nonparametric level estimation in nonstationary time series. Our approach applies to a broad class of level estimators expressible as weighted sample averages over time windows, including exponential smoothing methods and moving averages. The bootstrap procedure is motivated by asymptotic arguments and provides well-calibrated uniform-in-time coverage, enabling scalable uncertainty quantification in streaming or large-scale time-series settings. This makes the method suitable for tasks such as adaptive anomaly detection, online monitoring, or streaming A/B testing. Simulation studies demonstrate good finite-sample performance of our method across a range of nonstationary scenarios. In summary, this offers a practical resampling framework that complements online trend estimation with reliable statistical inference.

翻译：本文提出了一种用于非平稳时间序列中非参数水平估计的在线自助法方案。该方法适用于一大类可表示为时间窗口上加权样本平均值的水平估计量，包括指数平滑方法与移动平均。该自助法程序由渐近论证所驱动，能提供校准良好的时间均匀覆盖，从而在流式或大规模时间序列场景中实现可扩展的不确定性量化。这使得该方法适用于自适应异常检测、在线监测或流式A/B测试等任务。仿真研究表明，我们的方法在多种非平稳情境下均展现出良好的有限样本性能。总而言之，本文提供了一个实用的重抽样框架，能够为在线趋势估计提供可靠的统计推断补充。