发表机构
Ruhr-Universität Bochum（波鸿鲁尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出了高维函数型时间序列的同时变点推断框架，基于逐坐标累积和统计量与残差块乘子自助法，实现了变点的有效检测与定位，经模拟及实际数据验证了其性能。
AI 中文摘要
我们开发了一套用于高维函数型时间序列同时变点推断的框架。观测值被建模为时间依赖向量，其坐标取值于可能不同的可分希尔伯特空间，从而涵盖了广泛的函数型数据类别。异均值变化可能发生在坐标特定的位置，且坐标间的同期依赖关系不受限制。我们的方法基于逐坐标累积和统计量与残差块乘子自助法，该方法为全局检验及所有逐坐标决策提供了共同临界值。我们建立了非渐近高斯近似、在变化与未变化坐标任意混合下的强家族式错误控制的定量非渐近界、协方差自适应检测保证以及变点定位的同时高概率界。这些界适用于功能坐标数量以样本量的幂次指数增长的高维情形。我们通过模拟研究了有限样本性能，并利用河流流量曲线和高频金融对数收益率说明了该方法的有效性。
英文摘要
We develop a framework for simultaneous change-point inference of high-dimensional functional time series. The observations are modeled as temporally dependent vectors whose coordinates take values in possibly different separable Hilbert spaces, thereby covering a broad class of functional data. Heterogeneous mean changes may occur at coordinate-specific locations, and the contemporaneous dependence across coordinates is left unrestricted. Our procedure is based on coordinatewise cumulative-sum statistics and a residual block multiplier bootstrap that provides a common critical value for the global test and all coordinatewise decisions. We establish a nonasymptotic Gaussian approximation, quantitative nonasymptotic bounds for strong family-wise error control under arbitrary mixtures of changed and unchanged coordinates, covariance-adaptive detection guarantees, and simultaneous high-probability bounds for change-point localization. The bounds accommodate high-dimensional regimes in which the number of functional coordinates grows exponentially in a power of the sample size. We investigate finite-sample performance in simulations and illustrate the method using river discharge curves and high-frequency financial log returns.
CommentsMain paper: 25 pages. Supplement: 108 pages
