Asymptotic properties of recursive kernel density estimation for long-span high-frequency data

This article mainly studies the asymptotic properties of recursive kernel density estimation for high-frequency data with a long time span. Under appropriate conditions, the variance, bias, mean squared error, and optimal bandwidth are obtained. The asymptotic normality is proven by using moment inequalities for ρ-mixing high-frequency data. Numerical simulations show that the recursive kernel density estimation provides good fitting results for the invariant density function of the Vasicek diffusion process. Empirical analysis reveals that recursive kernel density estimation not only reflects the distribution characteristics of financial data but also allows us to fit parameter models by minimizing the squared deviation between the recursive kernel density estimation and the parameter model. It provides more applications for the financial field.