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 over the asset and time period. 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$\alpha$-th moments for any $\alpha>1$. 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.
翻译:开发了几种新的统计方法,以根据高频财务数据估算大型集成波动矩阵。 为了调查其无足轻重的波动行为, 需要为观察到的日志回报设定一个亚高端或有限的高端时间点假设, 这无法解释股票回报的重尾尾矿现象。 最近, 开发了一个强大的估算器, 处理重尾分配, 并有一些有约束的第四步假设。 然而, 我们经常观察到, 日志回归的尾部分布比限定的第四步运动的尾部分布更重, 尾部的重度程度在资产和时间段上各不相同。 在本文中, 要处理各种杂乱的重尾部分布, 我们开发了一个适应性强的综合波动估计仪, 使用跳动预测过程来应用适应性强的、 重尾尾部分配之前的波动( ARP) 。 我们显示, ARP 估算的下限的尾部样本样本样本浓度浓度浓度浓度水平是任何 美元\ a 的固定时间点, 和 IM IM 的常规估计是使用 最精确的 。