Adaptive Robust Large Volatility Matrix Estimation Based on High-Frequency Financial Data
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基于高频金融数据的大维波动率矩阵自适应稳健估计
- 研究问题
- 当高频收益的厚尾程度随资产和时间变化、甚至不具有限四阶矩时，如何稳健估计大维积分波动率矩阵？
- 方法与思路
- 作者在跳跃扩散设定下结合预平均与自适应截断构造 ARP 估计量，再借助近似因子模型和 POET 正则化估计大矩阵。
- 材料陈述的贡献
- 摘要称有限二倍 α 阶矩、α 大于一时可获得次 Weibull 尾集中界，并以匹配上下界说明相应估计程序的最优性。
- 阅读关注点
- 应核对矩条件约束的具体对象、尾指数适应和截断规则、跳跃与噪声处理，以及最优性界限和 POET 扩展的适用范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未经核验。摘要未展开完整条件和数值结果，所称最优性不能理解为所有厚尾环境下最优。
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 2$α$-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.