Online detection of distributional changes for time series in metric spaces
Abstract
We propose an online testing framework for detecting distributional changes in serially dependent data with values in a separable metric space. Based on two-sample U-statistics, the framework encompasses sequential analogs of energy distance and maximum mean discrepancy (MMD) procedures while accommodating temporal dependence. We establish asymptotic theory for finite and open-ended monitoring horizons that characterizes the full asymptotic run-length distribution under H0 and yields asymptotic false-alarm control. We further establish new spectral approximation results for kernel matrices formed from serially dependent observations, and use them to construct a feasible Monte Carlo calibration procedure. Our flexible window construction encompasses classical, Page-type, and full-scan historical-baseline monitoring and can achieve short detection delays for both early and late changepoints, without requiring sub-Gaussianity or high-order moments of the raw observations. Simulations show reliable false-alarm control across linear, nonlinear, high-dimensional, and functional time-series models and further demonstrate that, over a broad range of alternatives and changepoint locations, the proposed method can achieve substantially shorter delays than recent procedures designed specifically for rapid detection. Applications to foreign exchange rates, electricity-market curves, and daily air transportation networks illustrate the methodology across scalar, functional, and network-valued time series.
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BibTeX
@misc{boniece2026online,
title = {{Online detection of distributional changes for time series in metric spaces}},
author = {B. Cooper Boniece and Lajos Horváth and Lorenzo Trapani},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.26422},
eprint = {2608.26422},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26422},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Online detection of distributional changes for time series in metric spaces
AU - B. Cooper Boniece
AU - Lajos Horváth
AU - Lorenzo Trapani
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2608.26422
UR - https://arxiv.org/abs/2608.26422
AB - We propose an online testing framework for detecting distributional changes in serially dependent data with values in a separable metric space. Based on two-sample U-statistics, the framework encompasses sequential analogs of energy distance and maximum mean discrepancy (MMD) procedures while accommodating temporal dependence. We establish asymptotic theory for finite and open-ended monitoring horizons that characterizes the full asymptotic run-length distribution under H_0 and yields asymptotic false-alarm control. We further establish new spectral approximation results for kernel matrices formed from serially dependent observations, and use them to construct a feasible Monte Carlo calibration procedure. Our flexible window construction encompasses classical, Page-type, and full-scan historical-baseline monitoring and can achieve short detection delays for both early and late changepoints, without requiring sub-Gaussianity or high-order moments of the raw observations. Simulations show reliable false-alarm control across linear, nonlinear, high-dimensional, and functional time-series models and further demonstrate that, over a broad range of alternatives and changepoint locations, the proposed method can achieve substantially shorter delays than recent procedures designed specifically for rapid detection. Applications to foreign exchange rates, electricity-market curves, and daily air transportation networks illustrate the methodology across scalar, functional, and network-valued time series.
ER -