发表机构
Drexel University; University of Utah; University of Pavia（德雷塞尔大学; 犹他大学; 帕维亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对度量空间取值的序列相关时间序列，提出基于U统计量的在线分布变化检测框架，结合灵活窗口构造，在多类数据模型中实现可靠虚警控制与更短检测延迟，适用于标量、函数及网络值时间序列。
AI 中文摘要
我们提出了一种在线测试框架，用于检测取值于可分度量空间的序列相关数据中的分布变化。该框架基于两样本U统计量，包含能量距离和最大均值差异（MMD）方法的序列类似物，同时可容纳时间相关性。我们建立了有限和开放式监测范围的渐近理论，该理论刻画了原假设（H₀）下的完整渐近运行长度分布，并实现了渐近虚警控制。我们还建立了由序列相关观测构成的核矩阵的新谱近似结果，并将其用于构建可行的蒙特卡洛校准程序。我们灵活的窗口构造包含经典、Page型和全扫描历史基线监测，可对早期和后期变化点实现较短的检测延迟，无需原始观测的次高斯性或高阶矩。模拟结果显示，在线性、非线性、高维和函数时间序列模型中均实现了可靠的虚警控制，进一步证明，在广泛的备择假设和变化点位置范围内，所提方法相比近期专门为快速检测设计的方法可实现显著更短的延迟。将其应用于外汇汇率、电力市场曲线和每日航空运输网络，展示了该方法对标量、函数和网络值时间序列的适用性。
英文摘要
We propose an online testing framework for detecting distributional changes in serially dependent data with values in a separable metric space. Based on two-sample $U$-statistics, the framework encompasses sequential analogs of energy distance and maximum mean discrepancy (MMD) procedures while accommodating temporal dependence. We establish asymptotic theory for finite and open-ended monitoring horizons that characterizes the full asymptotic run-length distribution under $H_0$ and yields asymptotic false-alarm control. We further establish new spectral approximation results for kernel matrices formed from serially dependent observations, and use them to construct a feasible Monte Carlo calibration procedure. Our flexible window construction encompasses classical, Page-type, and full-scan historical-baseline monitoring and can achieve short detection delays for both early and late changepoints, without requiring sub-Gaussianity or high-order moments of the raw observations. Simulations show reliable false-alarm control across linear, nonlinear, high-dimensional, and functional time-series models and further demonstrate that, over a broad range of alternatives and changepoint locations, the proposed method can achieve substantially shorter delays than recent procedures designed specifically for rapid detection. Applications to foreign exchange rates, electricity-market curves, and daily air transportation networks illustrate the methodology across scalar, functional, and network-valued time series.
Commentssimulation details added; small typos fixed
