Asymptotic normality of kernel density estimation for mixing high-frequency data

Abstract

High-frequency data is widely used and studied in many fields. In this paper, the asymptotic normality of kernel density estimator under ρ-mixing high-frequency data is studied. We first derive some moment inequalities for mixing high-frequency data, and then use them to study the asymptotic normality of the kernel density estimator, and give Berry-Esseen upper bounds. The numerical simulations report that the kernel density estimation of high-frequency data has asymptotic normality, and the result is consistent with the theoretical conclusions. The actual data analysis shows that the kernel density estimation can well capture the characteristics of the distribution, and can use these features and the least square deviation principle to fit the parameter model, which is more convenient for further theoretical analysis and application analysis.