Abstract
This article investigates whether time-varying quantile regression curves are the same up to the horizontal shift or not. The errors and the covariates involved in the regression model are allowed to be locally stationary. We formalize this issue in a corresponding non-parametric hypothesis testing problem, and develop an integrated-squared-norm based test (SIT) as well as a simultaneous confidence band (SCB) approach. The asymptotic properties of SIT and SCB under null and local alternatives are derived. Moreover, the asymptotic properties of these tests are also studied when the compared data sets are dependent. We then propose valid wild bootstrap algorithms to implement SIT and SCB. Furthermore, the usefulness of the proposed methodology is illustrated via analysing simulated and real data related to COVID-19 outbreak.
Acknowledgment
Weichi Wu (corresponding author) is funded by NSFC (No.11901337) Young program and BJNSF (Z190001), and Subhra Sankar Dhar is funded by SERB project MATRICS (MTR/2019/000039), Government of India. The authors are grateful to the referees and the Associate Editor for their constructive comments on an earlier version of this paper. The authors would also like to thank Dr. Yeonwoo Rho for sharing their code to implement the algorithm proposed in their paper on unit root test.
Citation
Subhra Sankar Dhar. Weichi Wu. "Comparing time varying regression quantiles under shift invariance." Bernoulli 29 (2) 1527 - 1554, May 2023. https://doi.org/10.3150/22-BEJ1509
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