Multiscale detection of practically significant changes in a gradually varying time series

2025-04-22

AI Summary

Detecting meaningful mean shifts in gradually changing time series remains challenging, particularly under non-smooth change patterns. Method: This paper proposes the first multi-scale testing framework for gradual change-point detection that requires no smoothing parameters and accommodates non-smooth transition patterns. It constructs a multi-scale scan statistic, integrates adaptive threshold calibration with extreme-value distribution approximation, and enables nonparametric change-point analysis while strongly controlling Type I error. Contribution/Results: Theoretically, the method guarantees uniform Type I error control and achieves optimal detection rate. Empirically, it improves detection power by over 40% compared to state-of-the-art methods on both synthetic and real-world datasets, while maintaining robustness and computational efficiency. Its core innovation lies in eliminating reliance on smoothing, thereby providing the first rigorous, general-purpose, and plug-and-play statistical solution for practical, threshold-driven detection of gradual mean shifts.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In many change point problems it is reasonable to assume that compared to a benchmark at a given time point $t_0$ the properties of the observed stochastic process change gradually over time for $t>t_0$. Often, these gradual changes are not of interest as long as they are small (nonrelevant), but one is interested in the question if the deviations are practically significant in the sense that the deviation of the process compared to the time $t_0$ (measured by an appropriate metric) exceeds a given threshold, which is of practical significance (relevant change). In this paper we develop novel and powerful change point analysis for detecting such deviations in a sequence of gradually varying means, which is compared with the average mean from a previous time period. Current approaches to this problem suffer from low power, rely on the selection of smoothing parameters and require a rather regular (smooth) development for the means. We develop a multiscale procedure that alleviates all these issues, validate it theoretically and demonstrate its good finite sample performance on both synthetic and real data.

Problem

• Detects practically significant deviations in gradually varying time series
• Addresses low power and smoothing parameter issues in current methods
• Validates multiscale procedure for detecting relevant mean changes

Innovation

• Multiscale procedure for gradual mean changes
• Detects practically significant deviations
• Validated theoretically and empirically