Change-Point Detection for Heterogeneous High-Dimensional Functional Time Series
TL;DR
A novel Energy--PE statistic, which combines subject-wise squared CUSUM energy aggregation with a generalized power-enhancement component, is proposed, which controls size, improves power under sparse and sign-heterogeneous alternatives, and yields interpretable post-test summaries.
Abstract
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.