对象值时间序列的在线变点监测

中文摘要 AI 辅助

我们开发了用于监测对象值时间序列边际分布变化的闭端和开端程序。该方法结合了两种基于距离的希尔伯特空间嵌入、一个依赖于监测时间的投影以及自归一化。它完全可由成对距离计算，不需要长期方差估计，并允许精确的递归更新。在弱时间依赖下，闭端零极限是一个枢轴布朗泛函。对于无界时间范围内的监测，我们引入了一个增长的监测时间权重，建立了极大值不等式和均匀远端尾部控制，并推导出开端枢轴极限以及用于临界值模拟的等效固定区间表示。两种程序对固定边际变化都是一致的，并保留了与线性和二次投影信号相关的$n^{-1/2}$和$n^{-1/4}$局部检测边界。使用分布值时间序列的模拟展示了良好的数值性质，对月度股票收益分布的应用说明了我们程序的有效性。补充材料中报告了进一步使用图值时间序列的模拟以及对地震活动空间点过程的应用。

英文摘要

We develop closed- and open-end procedures for monitoring changes in the marginal distribution of object-valued time series. The method combines two distance-based Hilbert-space embeddings, a monitoring-time-dependent projection, and self-normalization. It is computable entirely from pairwise distances, does not require long-run variance estimation, and admits exact recursive updates. Under weak temporal dependence, the closed-end null limit is a pivotal Brownian functional. For monitoring over an unbounded horizon, we introduce a growing monitoring-time weight, establish a maximal inequality and uniform remote-tail control, and derive an open-end pivotal limit together with an equivalent fixed-interval representation for critical-value simulation. Both procedures are consistent against fixed marginal changes and retain the $n^{-1/2}$ and $n^{-1/4}$ local detection boundaries associated with the linear and quadratic projection signals. Simulations with distribution-valued time series illustrate favorable numerical properties, and an application to monthly stock-return distributions illustrates the usefulness of our procedure. Further simulations with graph-valued time series and an application to spatial point processes of seismic activity are reported in the supplementary material.

发表机构

• Washington University in St Louis（华盛顿大学圣路易斯分校）
• Aarhus University（奥胡斯大学）

机构由 AI 辅助整理，请以论文原文为准。