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 $2b$th moment for $b\in (1,2]$. 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.

中文翻译：

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高频金融数据程式化事实的波动率模型

本文介绍了新颖的波动扩散模型来解释高频金融数据的程式化事实，例如波动聚类、日内 U 形和杠杆效应。例如，所提出的波动率过程的每日综合波动率具有已实现的 GARCH 结构，对对数收益具有不对称影响。为了进一步解释财务数据的重尾性，我们假设对数收益有一个有限的$\mathrm{2个}b$的那一刻$b\in (\mathrm{1个},\mathrm{2个}]$. 然后，我们提出了一个 Huber 回归估计器，其最优收敛率为$n^{(\mathrm{1个}-b)/b}$. 我们还讨论了如何调整来自 Huber 损失的偏差并显示其渐近特性。