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

See all articles by Yongmiao Hong

Yongmiao Hong

Cornell University - Department of Economics

Brendan McCabe

University of Liverpool - Management School (ULMS)

Jiajing Sun

Chinese Academy of Sciences (CAS) - School of Economics and Management

Shouyang Wang

Chinese Academy of Sciences (CAS) - Center for Forecasting Science; Academy of Mathematics and Systems Sciences

Date Written: June 14, 2021

Abstract

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.

Suggested Citation

Hong, Yongmiao and McCabe, Brendan and Sun, Jiajing and Wang, Shouyang, Kolmogorov-Smirnov type statistics for structural breaks - a new adjusted-range based self-normalization approach (June 14, 2021). Available at SSRN: https://ssrn.com/abstract=3850894 or http://dx.doi.org/10.2139/ssrn.3850894

Yongmiao Hong

Cornell University - Department of Economics ( email )

Department of Statistical Science
414 Uris Hall
Ithaca, NY 14853-7601
United States
607-255-5130 (Phone)
607-255-2818 (Fax)

Brendan McCabe

University of Liverpool - Management School (ULMS) ( email )

Chatham Street
Liverpool, L69 7ZH
United Kingdom

Jiajing Sun (Contact Author)

Chinese Academy of Sciences (CAS) - School of Economics and Management ( email )

No.80, Zhongguancun East Road, Haidian District
Beijing
China

Shouyang Wang

Chinese Academy of Sciences (CAS) - Center for Forecasting Science; Academy of Mathematics and Systems Sciences ( email )

China

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