基于高频金融数据的自适应稳健大波动率矩阵估计
Adaptive Robust Large Volatility Matrix Estimation Based on High-Frequency Financial Data
AI总结：
针对高频金融数据中异质性重尾分布问题，本文提出自适应稳健预平均已实现波动率（ARP）估计量，证明其最优性并结合POET方法实现大规模积分波动率矩阵估计。
摘要：
基于高频金融数据，已有若干新颖的统计方法被提出用于估计大规模积分波动率矩阵。为了研究这些方法的渐近行为，它们通常要求观测到的对数收益率满足次高斯或有限高阶矩假设，这无法刻画股票收益的重尾现象。最近，一种稳健估计量被提出，用于在某种有界四阶矩假设下处理重尾分布。然而，我们经常观察到对数收益率的尾部比有限四阶矩更重，并且尾部厚重程度在不同资产之间以及随时间变化具有异质性。在本文中，为了处理异质性重尾分布，我们基于跳扩散过程，采用预平均和截断方案，提出了一种自适应稳健积分波动率估计量。我们将其称为自适应稳健预平均已实现波动率（ARP）估计量。我们证明，对于任意 $α>1$，ARP 估计量在仅具有有限 $2α$ 阶矩的条件下具有次威布尔尾部集中性质。此外，我们建立了匹配的上界和下界，以表明 ARP 估计过程是最优的。为了利用近似因子模型估计大规模积分波动率矩阵，我们进一步采用主正交补阈值（POET）方法对 ARP 估计量进行正则化。数值研究用于检验 ARP 估计量的有限样本表现。
英文摘要：
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.
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