发表机构
School of Mathematics, University of Bristol（布里斯托大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于移动和统计量的统一方法，用于高维矩阵时间序列中均值与协方差结构的多个变点同时检测，并通过理论与实验验证其有效性。
AI 中文摘要
本文研究高维矩阵值时间序列的一阶和二阶结构中同时发生的变点检测。具体地，我们将主效应因子模型的框架扩展以适应多个变点，使得均值和协方差结构中的变化分别由趋势平稳的主效应以及因子驱动的共同成分的变化来刻画。在此框架下，两类变化不一定对齐，且可以任意大而不会相互掩盖效应，每个检测到的变点都通过行或列分类进行标识，从而提高了其可解释性。我们提出了一种基于移动和统计量的统一程序来检测和定位这两类变化。在允许时间与横截面依赖的一般正则条件下，我们推导了所提方法的检测和定位保证。通过大量实验展示了该方法的有限样本性能，并通过纽约市黄色出租车行程记录的实际数据应用说明了其实用价值。
英文摘要
This paper studies simultaneous change point detection in the first- and second-order structures of high-dimensional matrix-valued time series. Specifically, we extend the framework of main effect factor models to accommodate multiple change points so that shifts in the mean and covariance structures are characterized by changes in the trend-stationary main effects main effects and in the factor-driven common components, respectively. Under this framework, the two types of changes are not necessarily aligned and can be arbitrarily large without masking the effects of each other, and each of the detected change points is identified either with the row or column categorizations which improves their interpretability. We propose a unified procedure based on moving-sum statistics to detect and localize both types of changes. Under general regularity conditions that allow for temporal and cross-sectional dependence, we derive detection and localization guarantees for the proposed method. The finite-sample performance of the method is demonstrated through extensive experiments, and its practical usefulness is illustrated by a real data application to New York City Yellow Taxi trip records.
