Adaptive robust large volatility matrix estimation based on high-frequency financial data
基于高频金融数据的大型波动率矩阵自适应稳健估计AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确使用高频收益估计积分波动率矩阵，并结合近似因子模型与 POET 正则化。
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基于高频金融数据的大型波动率矩阵自适应稳健估计
- 研究问题
- 当资产收益具有跨资产、跨时间异质的重尾特征，甚至不满足有限四阶矩条件时，如何可靠估计高维积分波动率矩阵？
- 方法与思路
- 作者在跳跃扩散过程下结合预平均与截断构造 ARP 估计量，再利用近似因子模型和 POET 方法对大型积分波动率矩阵进行正则化。
- 材料陈述的贡献
- 摘要称，在有限二倍 α 阶矩、α 大于一的条件下获得次 Weibull 尾部集中性，并给出匹配的上下界以说明最优性及数值研究。
- 阅读关注点
- 应核对尾部异质性的刻画、自适应截断参数如何确定、最优性对应的损失与模型类，以及高频观测误差和跳跃进入理论的方式。
- 阅读边界
- 所给 RePEc 出版社摘要未列出完整采样、依赖及因子条件，也未报告数值改善幅度；最优性不能外推到所有情形，其他版本变化未知。
原文摘要
Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order moment assumption for observed log-returns, which cannot account for the heavy-tail phenomenon of stock-returns. Recently, a robust estimator was developed to handle heavy-tailed distributions with some bounded fourth-moment assumption. However, we often observe that log-returns have heavier tail distribution than the finite fourth-moment and that the degrees of heaviness of tails are heterogeneous across asset and over time. In this paper, to deal with the heterogeneous heavy-tailed distributions, we develop an adaptive robust integrated volatility estimator that employs pre-averaging and truncation schemes based on jump-diffusion processes. We call this an adaptive robust pre-averaging realized volatility (ARP) estimator. We show that the ARP estimator has a sub-Weibull tail concentration with only finite 2α-th moments for any α>1. In addition, we establish matching upper and lower bounds to show that the ARP estimation procedure is optimal. To estimate large integrated volatility matrices using the approximate factor model, the ARP estimator is further regularized using the principal orthogonal complement thresholding (POET) method. The numerical study is conducted to check the finite sample performance of the ARP estimator.