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

Yongmiao Hong, Oliver Linton, Brendan McCabe, Jiajing Sun*, Shouyang Wang

*Corresponding author for this work

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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 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.
Original languageEnglish
Article number105603
Number of pages19
JournalJournal of Econometrics
Volume238
Issue number2
Early online date9 Nov 2023
DOIs
Publication statusPublished - Jan 2024

Bibliographical note

Acknowledgments:
The research is supported by National Natural Science Foundation of China (NSFC) grants No. 71988101 and No. 72173120. We would like to thank Serena Ng (Editor), an associate editor, two anonymous referees, as well as the participants at Gregory Chow Seminar in Center of Forecasting Sciences, Chinese Academy of Sciences, and Paula and Gregory Chow Institute for Studies in Economics, Xiamen University (2023), Australian Meeting of the Econometric Society (2021), North American Summer Meeting of the Econometric Society (2021) and the 4th International Conference on Computational and Financial Econometrics, for their insightful comments and suggestions, which have led to significant improvements to our paper.

Keywords

  • Change-point testing
  • CUSUM process
  • Parameter constancy
  • Studentization

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