Optimal detection of general moment changes: Simultaneous mean and covariance change detection and beyond
Abstract
We study multiple change-point detection in multivariate time series whose distributions change in a piecewise constant manner. Distributional changes can manifest across different moment orders, from shifts in the mean and covariance to changes in higher-order moments. Higher-order moments capture increasingly rich distributional features but become difficult to estimate in high dimensions. Our tensor representation unifies moments of different orders within a common linear algebraic framework, enabling a new method to detect changes in moments of all orders up to a prescribed fixed order p. The resulting procedure accommodates temporal dependence and allows the dimension of the time series to grow with the sample size. Under suitable regularity conditions, the proposed procedure achieves a localization error rate that matches a newly developed minimax lower bound. We further derive limiting distributions under both nonvanishing and vanishing moment jumps and construct asymptotically valid confidence intervals in the vanishing-jump regime. Numerical experiments and real-data analyses demonstrate the method's effectiveness in detecting moment changes and a range of distributional shifts.
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BibTeX
@misc{luo2026optimal,
title = {{Optimal detection of general moment changes: Simultaneous mean and covariance change detection and beyond}},
author = {Xiaokai Luo and Chenghao Xu and Haotian Xu and Carlos Misael Madrid Padilla and Daren Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36594},
eprint = {2609.36594},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36594},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal detection of general moment changes: Simultaneous mean and covariance change detection and beyond
AU - Xiaokai Luo
AU - Chenghao Xu
AU - Haotian Xu
AU - Carlos Misael Madrid Padilla
AU - Daren Wang
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36594
UR - https://arxiv.org/abs/2609.36594
AB - We study multiple change-point detection in multivariate time series whose distributions change in a piecewise constant manner. Distributional changes can manifest across different moment orders, from shifts in the mean and covariance to changes in higher-order moments. Higher-order moments capture increasingly rich distributional features but become difficult to estimate in high dimensions. Our tensor representation unifies moments of different orders within a common linear algebraic framework, enabling a new method to detect changes in moments of all orders up to a prescribed fixed order p. The resulting procedure accommodates temporal dependence and allows the dimension of the time series to grow with the sample size. Under suitable regularity conditions, the proposed procedure achieves a localization error rate that matches a newly developed minimax lower bound. We further derive limiting distributions under both nonvanishing and vanishing moment jumps and construct asymptotically valid confidence intervals in the vanishing-jump regime. Numerical experiments and real-data analyses demonstrate the method's effectiveness in detecting moment changes and a range of distributional shifts.
ER -