Kolmogorov–Smirnov type testing for structural breaks: A new adjusted-range based self-normalization approach
提出一种基于调整极差的自标准化方法，用于时间序列结构突变检验，对持久自相关、异方差、单位根和异常值具有稳健性，能改善现有方法的功效下降问题。
A popular self-normalization (SN) approach in time series analysis uses the variance of a partial sum as a self-normalizer. This is known to be sensitive to irregularities such as persistent autocorrelation, heteroskedasticity, unit roots and outliers. We propose a novel SN approach based on the adjusted-range of a partial sum, which is robust to these aforementioned irregularities. We develop an adjusted-range based Kolmogorov-Smirnov type test for structural breaks for both univariate and multivariate time series, and consider testing parameter constancy in a time series regression setting. Our approach can rectify the well-known power decrease issue associated with existing self-normalized KS tests without having to use backward and forward summations as in Shao and Zhang (2010), and can alleviate the “better size but less power” phenomenon when the existing SN approaches (Shao, 2010; Zhang et al., 2011; Wang and Shao, 2022) are used. Moreover, our proposed tests can cater for more general alternatives. Monte Carlo simulations and empirical studies demonstrate the merits of our approach.