A0402
Title: Adaptive robust large volatility matrix estimation based on high-frequency financial data
Authors: Donggyu Kim - KAIST (Korea, South) [presenting]
Abstract: Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. They require sub-Gaussian or finite high-order moments assumptions for observed log-returns, which cannot account for the heavy tail phenomenon of stock returns. Recently, the robust estimator is developed to handle the heavy-tailed distributions with bounded fourth moments assumption. However, we often observe that the tail index of observed log-returns is less than 4, and the heavy-tailedness are heterogeneous over the asset and time period. To deal with the heterogeneous heavy-tailed distributions, we develop an adaptive robust integrated volatility estimator which employs pre-averaging and truncation schemes according to the daily tail indexes. We call this adaptive robust pre-averaging realized volatility (ARP) estimator. We show that the ARP estimator has the sub-Gaussian tail concentration with only finite 2$\alpha$-moments for any $\alpha>1$. In addition, we establish matching upper and lower bounds to show that the estimation procedure is optimal. To estimate large integrated volatility matrices using the approximate factor model, the ARP estimator is further regularized by the principal orthogonal complement thresholding method (POET). The numerical study is conducted to check the finite sample performance of the ARP estimator.
