Functional index coefficient models for locally stationary time series

Abstract

In the analysis of nonlinear time series, we propose a novel functional index coefficient model for the locally stationary data. The proposed model can effectively capture the dynamic interaction effects between variables and the nature of data evolution. Drawing the idea from the spline-backfitted method, we propose a three-step estimation procedure and establish the asymptotic properties of the resulting nonparametric estimators. We further construct simultaneous confidence bands for the time-varying functions to explore the global variation of the original data. We also develop a test statistic to check the time-varying properties based on a bootstrap procedure. Simulation studies have been conducted to investigate the finite sample performance of the proposed methods. Two real applications in the finance market and the Hong Kong respiratory and circulatory disease data are analysed for illustration.

Keywords:

• Dynamic interaction effect
• hypothesis testing
• locally stationary
• time-varying
• simultaneous confidence band

Mathematics Subject Classifications:

• 62G05
• 62G10

Acknowledgments

The authors sincerely thank the editor and two reviewers for providing feedback and constructive comments and suggestions that greatly improved the quality of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of You was supported in part by the National Natural Science Foundation of China [grant number 11971291]. The research of Zhou was supported by the State Key Program of National Natural Science Foundation of China [grant number 71931004] and the State Key Program in the Major Research Plan of National Natural Science Foundation of China [grant number, 91546202]. The research of Xu was supported by Projects of National Social Science Fund of China [grant number 19BTJ032].