【专家简介】 王汉超，山东大学教授，博士生导师, 山东大学金融研究院院长助理。主要从事概率统计极限理论及其应用的研究，特别在弱收敛，集中不等式与金融统计等领域发表了若干文章。与林正炎教授合作，在新加坡世界科技出版社出版专著 Weak Convergence and Its Applications。与于志勇教授合作，在高等教育出版社出版教材《应用随机分析》。近几年来，在概率论，数理统计，计量经济等领域权威期刊上发表论文近二十篇。主持国家自然科学基金两项，作为骨干成员，参加国家重点研发计划项目两项。
【报告摘要】We consider estimating instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalized shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literature. The uniform consistency property is derived for the proposed spot volatility matrix estimator with convergence rates comparable to the optimal minimax one. For the high-frequency data contaminated by the microstructure noise, we introduce a localized pre-averaging estimation method in the high-dimensional setting which first pre-whitens data via a kernel filter and then uses the estimation tool developed in the noise-free scenario, and further derive the uniform convergence rates for the developed spot volatility matrix estimator. We also combine the kernel smoothing with the shrinkage technique to estimate the time-varying volatility matrix of the high-dimensional noise vector, and establish the relevant uniform consistency result. In addition, we consider large spot volatility matrix estimation in time-varying factor models and derive the uniform convergence property. Numerical studies are provided to examine performance of the proposed estimation methods in finite samples. This talk is based on a joint work with Bu, Li and Linton.