Bootstrap bandwidth selection in time-varying coefficient models with jumps

Abstract

The time-varying coefficient models (TVCMs) are very important tools to explore the hidden structure between the time series response variable and its predictors. The assumption that the coefficient functions are smooth can be restrictive in practice. The TVCMs with jumps are needed to be considered. Selection of smoothing parameters plays a critical role in assessing the performance of estimations of coefficient functions. In this article, we first develop a nonparametric two-step estimation procedure for estimating a finite number of jumps of the coefficient functions. Then, based on the estimated jumps, we propose a bootstrapping bandwidth selection procedure in the TVCMs with jumps. Monte Carlo simulations are conducted to evaluate the finite sample performance of the proposed data-driven estimation and bootstrap bandwidth selection procedures. As an illustration, the proposed methodologies are further applied to a real data example.

Keywords:

• Bandwidth selection
• bootstrap
• jumps
• time-varying coefficient models

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H12
• 62A10

Acknowledgments

The authors are grateful to the editor, the associate editor and two anonymous referees for their constructive comments which have greatly improved this paper.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China under Grants Nos. 11701286, 11971235, 11961038, and 11571073, the Natural Science Foundation of Jiangsu Province of China under Grant No. BK20171073, the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No. 17KJB110006, and Xuzhou University of Technology Research Funds No. XKY2018120.