报 告 人：孔新兵 教授（苏州大学高等统计与计量经济中心）
报告题目：HOW MANY COMMON DRIVING BROWNIAN MOTIONS LATENT IN HIGH DIMENSIONAL ITO PROCESS WITH HIGH FREQUENCY DATA?
报告时间：2015年12月17日上午10:00
报告地点：静远楼1506学术报告厅
摘要：In this paper, we find a novel approach to determine the number of common driving Brownian motions latent in the high dimensional Ito process using high frequency data. The high dimensional Ito process is first approximated locally on a shrinking block by discrete-time approximate factor model. We then estimate the number of common driving Brownian motions by minimizing the penalized aggregated mean-squared residual error. It turns out the estimated number is consistent to the true number. While the local mean-squared residual error on each block converges at the rate of $n^{1/4} \wedge \sqrt{p} $ where $n$ is the sample size and $p$ is the dimensionality, it is interesting that the aggregated mean-squared residual error converges at a higher rate of $\sqrt{n}\wedge p$. It is also shown that the model discretization error does not affect the estimation at all when the block length shrinks to zero. Simulation results justify the performance of our estimator. A real financial data is also analyzed.
孔新兵教授简介：孔新兵,现为苏州大学高等统计与计量经济中心特聘教授，博士生导师。研究方向为高频数据统计推断，高维矩阵分析，多重检验。在Ann. Stat., JASA, JOE, JBES, ET，Sinica，等杂志发表论文多篇。获香港数学会优秀博士毕业论文，复旦青年教师新星奖，江苏省双创博士等荣誉。