SCAN: Sequentially Detecting Change-points via Adaptive Nonparametric Inference

2026-08-28

AI Summary

SCAN方法通过自适应非参数推理在长且序列依赖的单变量时间序列中检测多个分布变化点，使用整体窗口大小减少对窗口大小和阈值设定的敏感性。

Abstract

Modern time series are often long, serially dependent, and non-stationary. Existing change-point methods either target specific changes or become computationally intensive when using nonparametric costs on long series. Many also require thresholds to be carefully calibrated under serial dependence. We introduce SCAN, an offline method for detecting multiple distributional change-points in long, serially dependent univariate time series. SCAN compares adjacent windows using an integral probability metric, calibrates local discrepancies with a dependence-aware bootstrap, and refines candidate locations using a scaled 1-Wasserstein criterion, enabling detection of changes in mean, variance, and broader distributional structure within a unified framework. An ensemble over multiple window sizes reduces sensitivity to window size and threshold specification. We establish consistency of the estimated number and locations of change-points under exponential alpha-mixing dependence, and show that the localization statistic reduces to a CUSUM-type statistic under pure mean shifts. In simulations with up to one million observations, SCAN generally achieves higher covering and F1-scores than competing methods across mean and joint mean-variance shifts, particularly under serial dependence. On real data, SCAN identifies labeled activity transitions in sensor data and interpretable structural changes in hourly Bitcoin prices. Implementations are available in the Python package scan-cpd and R package scanr.

Problem

• change-point detection
• serial dependence
• nonparametric inference
• time series
• long sequences

Innovation

• integral probability metric
• dependence-aware bootstrap
• scaled 1-Wasserstein criterion
• ensemble over multiple window sizes