Kolmogorov-Smirnov type testing for structural breaks: A new adjusted-range based self-normalization approach

77 Pages Posted: 27 May 2021 Last revised: 17 Apr 2023

See all articles by Yongmiao Hong

Yongmiao Hong

Cornell University - Department of Economics

Oliver B. Linton

University of Cambridge

Brendan McCabe

University of Liverpool - Management School (ULMS)

Jiajing Sun

School of Mathematics, University of Birmingham

Shouyang Wang

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

Date Written: June 9, 2023

Abstract

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 root and outliers. We propose a novel SN approach based on the adjusted-range of a partial sum, which is robust to the 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.

Keywords: Change-point testing; CUSUM process; Parameter constancy; Studentization.

Suggested Citation

Hong, Yongmiao and Linton, Oliver B. and McCabe, Brendan and Sun, Jiajing and Wang, Shouyang, Kolmogorov-Smirnov type testing for structural breaks: A new adjusted-range based self-normalization approach (June 9, 2023). 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)

Oliver B. Linton

University of Cambridge ( email )

Faculty of Economics
Cambridge, CB3 9DD
United Kingdom

Brendan McCabe

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

Chatham Street
Liverpool, L69 7ZH
United Kingdom

Jiajing Sun (Contact Author)

School of Mathematics, University of Birmingham ( email )

School of Mathematics Watson Building University o
Birmingham, B15 2TT
Great Britain

Shouyang Wang

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

China

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