Asymptotic normality of Nadaraya–Waton kernel regression estimation for mixing high-frequency data

Abstract

High-frequency data is widely used and studied in many fields, especially in the econometrics and statistics. In this paper, the asymptotic normality of Nadaraya–Waton (NW) kernel regression estimator under ρ-mixing high-frequency data is studied. We first derive some moment inequalities for ρ-mixing high-frequency data, and then use them to study the asymptotic normality of NW kernel regression estimator, and give Berry–Esseen upper bounds. The numerical simulations report that the kernel regression estimator of high-frequency data has good asymptotic normality. Our empirical analysis is to fit the correlation between the five minute interval price increment and the corresponding trading volume for the Shanghai Stock Exchange Index, Entrepreneurship Index and Real Estate Index. These kernel regression curves better reflect people's investment behaviour.

Keywords:

• High-frequency data
• mixing samples
• Nadaraya–Waton kernel regression estimator
• asymptotic normality

Mathematics Subject Classification (2000):

• 62G08
• 60F05

Acknowledgments

The authors are grateful to the referees and the editor for their valuable comments, which improved the structure and the presentation of the paper.

Disclosure statement

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

Additional information

Funding

This research was supported by Guangxi Natural Science Foundation (No. 2022GXNSFAA035516) and the Natural Science Foundation of China (No. 11461009); Innovation Project of Guangxi Graduate Education [XYCSR2023015].