由国际合作处资助,应哈工大数学系陈佳奇老师的邀请，香港大学姚建峰教授将于近日来访我校并做报告，以下是报告信息，欢迎感兴趣的师生参加。

报告题目1：On a spiked model for large volatility matrix estimation from noisy high-frequency data

报告题目2：Forecasting High-Dimensional Realized Volatility Matrices Using A Factor Model

时 间: 2019.01.02, 9:00-12:00，

地 点：格物楼503室

报告题目3：On structure testing for component covariance matrices of a highdimensional mixture

时 间：2019.01.02, 14:30-16:00，

地 点：正心215室

报告摘要：

1.Recently, inference about high-dimensional integrated covariance matrices (ICVs) based on noisy high-frequency data has emerged as a challenging problem. Using the large-dimensional random matrix theory, it has been established that the eigenvalue distribution of the pre-averaging estimator(PA-RCov)matrix is intimately linked to that of the ICV through the Marcenko-Pastur equation. Consequently, the spectrum of the ICV can be inferred from that of the PA-RCov.

2. Modeling and forecasting covariance matrices of asset returns play a crucial role in many financial fields, such as portfolio allocation and asset pricing. We propose a factor model with a diagonal CAW model for the factor realized covariance matrices. Consequently, the positive definiteness of the estimated covariance matrix is ensured with the proposed model. Asymptotic theory is derived for the estimated parameters. In the extensive empirical analysis, we find that the number of parameters can be reduced significantly; it is only about one-tenth of the benchmark model.

3 By studying the family of p-dimensional scale mixtures, this paper shows for the first time a non trivial example where the eigenvalue distribution of the corresponding sample covariance matrix does not converge to the celebrated Marcenko-Pastur law. We establish a novel and general CLT for linear statistics of eigenvalues of the sample covariance matrix.

专家简介：姚建峰教授，现籍法国，原籍常熟杨园，1979年江苏省高考状元，经国家选拔到法国留学，就读于巴黎第十一大学数学系，先后获得学士、硕士和应用数学博士学位，1999年在巴黎第一大学获得应用数学HDR文凭（相当于先前法国国家博士文凭）。先后任教巴黎大学、雷恩大学与香港大学。现担任法国雷恩一大数学学院和香港大学统计与精算学系教授。目前研究方向包括：大维随机矩阵分析，非线性时间序列，以及图像处理和数学分析等。在国际顶尖杂志发表论文七十余篇，其中包括Annals of Statistics, Annals of Applied Probability, Biometrika, Journal of the Royal Statistical Society Series B和SIAM Journal on Imaging Science等。