We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully nonparametric, enjoys effortless tuning and is robust to temporal dependence. One salient and distinct feature of the proposed method is its versatility, where it allows change-point detection for a broad class of parameters (such as mean, variance, correlation and quantile) in a unified fashion. At the core of our method, we couple the self-normalization (SN) based tests with a novel nested local-window segmentation algorithm, which seems new in the growing literature of change-point analysis. Due to the presence of an inconsistent long-run variance estimator in the SN test, non-standard theoretical arguments are further developed to derive the consistency and convergence rate of the proposed SN-based change-point detection method. Extensive numerical experiments and relevant real data analysis are conducted to illustrate the effectiveness and broad applicability of our proposed method in comparison with state-of-the-art approaches in the literature.
翻译:我们建议了一个在多变时间序列中进行变化点估计的新而统一的框架。拟议方法完全不对称,进行不努力的调整,并且具有很强的时间依赖性。拟议方法的一个突出和独特的特征是其多功能性,它允许以统一的方式为广泛的参数类别(如平均值、差异、相关性和四分法)进行变化点检测。在我们的方法的核心,我们把基于自我正常化(SN)的测试与新颖的嵌巢式本地窗口分割算法结合起来,这种算法在变化点分析的文献中看来是新的。由于在SN测试中存在不一致的长期差异估计,因此进一步开发了非标准的理论论点,以得出拟议的基于SN的改变点检测方法的一致性和趋同率。我们进行了广泛的数字实验和相关的实际数据分析,以说明我们拟议方法与文献中的最新方法相比的有效性和广泛适用性。