Kolmogorov-Smirnov type statistics for structural breaks - a new adjusted-range based self-normalization approach
44 Pages Posted: 27 May 2021 Last revised: 27 Dec 2021
Date Written: June 14, 2021
In this paper, we propose a self-normalization approach based on the adjusted- range of a partial sum. We first introduce adjusted-range based Kolmogorov-Smirnov (KS) type statistics to test for structural breaks in the mean of a univariate time series. We then present the extended KS statistic (EKS) for testing structural breaks in a more general setting, which includes the marginal mean, the marginal variance, the autocorrelation function, quantiles and the spectrum as special cases. Our approach can rectify the well known power decrease issue associated with self-normalized KS tests without the use of backward and forward summation as in the G statistic of Shao and Zhang (2010). It also circumvents the specification of a contrast process as in Zhang and Lavitas (2018). Furthermore, our proposed test statistics are portmanteau and can cater for general alternatives, whereas the G test statistic in Shao and Zhang (2010) requires the knowledge of the number of structural breaks. Finally, Monte Carlo simulations indicate that our proposed KS-type statistics can address the “better size but less power” phenomenon (Wang and Shao, 2020) exhibited by existing self-normalized test statistics. The empirical studies also indicate the adequacy of our proposed method.
Keywords: Change-point testing; CUSUM process; Portmanteau test; Studentization.
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