Recursive Multiple Change Point Detection of Nonstationary Time Series: Instability Tests, Estimation and Confidence Intervals

Abstract: We develop bootstrap-assisted robust binary segmentation (BARBS), a recursive binary segmentation method for multiple change point detection under general nonstationary temporal dynamics. A novel Gaussian multiplier bootstrap for the CUSUM statistics is proposed, offering robustness to complex dependence structures. Through meticulous calibration of the critical values at each stage of the recursion, BARBS ensures control of the Type I error under the null hypothesis of no change points. When change points are present, BARBS identifies the correct number of changes with a prespecified probability, and the resulting change point location estimators attain the same uniform consistency rate as classical binary segmentation. Building on this, we introduce second-stage refined estimators that achieve the optimal individual localization rate, and establish their asymptotic distributions and nearly optimal uniform localization rates under both fixed and vanishing jump magnitudes. Extensive numerical experiments across various settings confirm the robustness and superior performance of BARBS relative to existing approaches. To illustrate the practical relevance of the proposed methodology, we analyze U.S. inflation data, yielding change points that align with several documented macroeconomic episodes.