Adaptive Robust Large Volatility Matrix Estimation Based on High-Frequency Financial Data

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 the heavy tail phenomenon of stock returns. Recently, robust estimator was handle heavy-tailed distributions with some bounded fourth-moment assumption. However, we often observe that log-returns heavier distribution than and degrees heaviness tails are heterogeneous over asset time period. In this paper, deal distributions, develop an adaptive employs pre-averaging truncation schemes jump-diffusion processes. We call realized (ARP) estimator. show ARP has sub-Weibull concentration only 2?-th moments any ? > 1. addition, establish matching upper lower bounds estimation procedure is optimal. using approximate factor model, further regularized principal orthogonal complement thresholding (POET) method. The numerical study conducted check sample performance