异质性高维函数时间序列的变点检测
Change-Point Detection for Heterogeneous High-Dimensional Functional Time Series
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中文总结 AI 辅助
针对高维函数时间序列变点检测中传统方法的信号衰减问题，提出Energy-PE统计量并结合聚类算法，经数值和股票应用验证其功效更优且可解释。
中文摘要 AI 辅助
高维函数面板由跨多个主体观测的时间有序曲线组成，自然呈现异质性结构变化。在主体层面的稀疏断点信号或符号相反的偏移下，传统均值聚合CUSUM方法可能因截面平均导致的信号衰减或抵消而出现明显的功效损失。我们提出一种新颖的Energy-PE统计量，它将逐主体平方CUSUM能量聚合与广义功效增强分量相结合。能量聚合在符号异质性变化下保留主体层面的证据，而功效增强分量则提升对稀疏弱断点信号的敏感性。在正则条件下，我们建立了所提统计量的渐近性质。我们进一步结合潜在组结构和基于信息准则的聚类算法，以估计异质性断点的未知组数量和成员身份。数值研究和日内股票应用表明，Energy-PE可控制大小，在稀疏和符号异质性备择假设下提升功效，并产生可解释的后验检验摘要。
英文摘要
High-dimensional functional panels consist of temporally ordered curves observed across many subjects and naturally exhibit heterogeneous structural changes. Under sparse subject-level break signals or opposite-signed shifts, traditional mean-aggregated CUSUM procedures may suffer noticeable power loss due to signal attenuation or cancellation induced by cross-sectional averaging. We propose a novel Energy--PE statistic, which combines subject-wise squared CUSUM energy aggregation with a generalized power-enhancement component. The energy aggregation preserves subject-level evidence under sign-heterogeneous changes, while the power-enhancement component improves sensitivity to sparse weak break signals. Under regularity conditions, we establish the asymptotic behavior of the proposed statistic. We further incorporate a latent group structure and an information-criterion-based clustering algorithm to estimate the unknown group number and membership for heterogeneous break points. Numerical studies and an intraday stock application demonstrate that Energy--PE controls size, improves power under sparse and sign-heterogeneous alternatives, and yields interpretable post-test summaries.
