Volatility models for stylized facts of high-frequency financial data

This article introduces novel volatility diffusion models to account for the stylized facts of high-frequency financial data such as volatility clustering, intraday U-shape, and leverage effect. For example, the daily integrated volatility of the proposed volatility process has a realized GARCH structure with an asymmetric effect on log returns. To further explain the heavy-tailedness of the financial data, we assume that the log returns have a finite 2bth moment for b is an element of(1,2]. Then, we propose a Huber regression estimator that has an optimal convergence rate of n(1-b)/b. We also discuss how to adjust bias coming from Huber loss and show its asymptotic properties.