科学研究

Dr. Liu is a professor of econometrics at Wuhan University. He got his Ph.D. degree from National University of Singapore in 2013. His research interests include financial econometrics, theoretical econometrics, and data science. His works have been published on the top journals of statistics and economics such as Journal of the American Statistical Association and Journal of Econometrics. 

We consider high-dimensional measurement errors with high-frequency data. Our focus is on recovering the covariance matrix of the random errors with optimality. In this problem,  not all components of the random vector are observed at the same time and the measurement errors are latent variables, leading to major challenges besides high data dimensionality. We first propose a  new covariance matrix estimator in this context with appropriate localization and thresholding, and then conduct a series of comprehensive theoretical investigations of the proposed estimator. By developing a new technical device integrating the high-frequency data feature with the conventional notion of alpha-mixing, our analysis successfully accommodates the challenging serial dependence in the measurement errors. Our theoretical analysis establishes the minimax optimal convergence rates associated with two commonly used loss functions.  We then establish cases when the proposed localized estimator with thresholding achieves the minimax optimal convergence rates. Considering that the variances and covariances can be small in reality, we conduct a second-order theoretical analysis that further disentangles the dominating bias in the estimator. A bias-corrected estimator is then proposed to ensure its practical finite sample performance. To accommodate jumps, we extensively analyze our estimator in a setting with both jumps and stochastic volatility and show that they are reasonably robust. We illustrate the promising empirical performance of the proposed estimator with extensive simulation studies and a real data analysis.