Stationarity of Manifold Time Series

• 成果类型: Article; Early Access
• 署名作者: Zhu, Junhao; Kong, Dehan; Zhang, Zhaolei; Lin, Zhenhua
• 署名单位: University of Toronto; National University of Singapore
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2628344
• 发表日期: 2026-05-27
• 关键词: Bootstrap; CURVATURE; Cusum; spectral density; sphere; gaussian approximations; Fréchet Regression; point

摘要

In modern interdisciplinary research, manifold time series data have been garnering more attention. A critical question in analyzing such data is stationarity, which reflects the underlying dynamic behavior and is crucial across various fields like cell biology, neuroscience and empirical finance. Yet, there has been an absence of a formal definition of stationarity that is tailored to manifold time series. This work bridges this gap by proposing the first definitions of first-order and second-order stationarity for manifold time series. Additionally, we develop novel statistical procedures to test the stationarity of manifold time series and study their asymptotic properties. Our methods account for the curved nature of manifolds, leading to a more intricate analysis than that in Euclidean space. The effectiveness of our methods is evaluated through numerical simulations and their practical merits are demonstrated through analyzing a cell-type proportion time series dataset from a paper recently published in Cell. The first-order stationarity test result aligns with the biological findings of this article, while the second-order stationarity test provides numerical support for a critical assumption made therein. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.