Bootstrap-based inference for multiple mean-variance changepoint models

Identifying multiple change points in the mean and/or variance is crucial across various fields, including finance and quality control. We introduce a novel technique that detects change points for the mean and/or variance of a noisy sequence and constructs confidence intervals for both the mean and variance of the sequence. This method integrates the weighted bootstrap with the Sequential Binary Segmentation (SBS) algorithm. Not only does our technique pinpoint the location and number of change points, but it also determines the type of change for each estimated point, specifying whether the change occurred in the mean, variance, or both. Our simulations show that our method outperforms other approaches in most scenarios, clearly demonstrating its superiority. Finally, we apply our technique to three datasets, including DNA copy number variation, stock volume, and traffic flow data, further validating its practical utility and wide-ranging applicability.

针对含噪序列的均值与/或方差开展多个变点（change point）识别，在金融、质量控制等诸多领域均具备关键应用价值。本文提出一种新颖的变点检测方法，可对含噪序列的均值和/或方差进行变点检测，并为该序列的均值与方差构建置信区间。该方法将加权自助法（weighted bootstrap）与顺序二元分割（Sequential Binary Segmentation，SBS）算法相结合。本方法不仅能够精准定位变点的位置与数量，还可判定每个估计变点的变化类型，明确该变化仅发生于均值、仅发生于方差，抑或二者兼具。仿真实验结果表明，在多数场景下本文所提方法的性能优于其他同类方法，清晰验证了其优越性。最后，本文将所提方法应用于三类数据集，涵盖DNA拷贝数变异（DNA copy number variation）、股票成交量与交通流量数据，进一步验证了该方法的实用价值与广泛适用性。