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∈(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.