In this paper, we propose two bootstrap procedures, namely parametric and block bootstrap, to approximate the finite sample distribution of change-point estimators for piecewise stationary time series. The bootstrap procedures are then used to develop a generalized likelihood ratio scan method (GLRSM) for multiple change-point inference in piecewise stationary time series, which estimates the number and locations of change-points and provides a confidence interval for each change-point. The computational complexity of using GLRSM for multiple change-point detection is as low as $O(n(\log n)^{3})$ for a series of length n. Extensive simulation studies are provided to demonstrate the effectiveness of the proposed methodology under different scenarios. Applications to financial time series are also illustrated.

在本文中，我们提出了两个引导程序，即参数引导程序和块引导程序，以近似分段平稳时间序列的变化点估计器的有限样本分布。然后使用引导程序开发一种广义似然比扫描方法 (GLRSM)，用于分段平稳时间序列中的多个变化点推断，该方法估计变化点的数量和位置，并为每个变化点提供置信区间。使用 GLRSM 进行多个变化点检测的计算复杂度低至 $O(n(\log n)^{3})$ 对于一系列长度n. 提供了广泛的模拟研究来证明所提出的方法在不同场景下的有效性。还说明了金融时间序列的应用。