1，金融数据的主成分分析法，
报告人：汪四水 金融工程研究中心教授，
时间：11月10号（周二）晚上06:30--07:30
地点：金融工程研究中心105
报告摘要：主成分分析是一类重要的多元统计分析方法，可以将高维数据进行降维，因而有着广泛的应用。本报告将给出主成分分析方法的原理，主要结果及计算步骤，最后再给出其在金融及其他方面的一些应用例子。
 
2.大面板高频金融数据的因子结构分析
报告人：孔新兵 统计与计量经济研究中心教授
时间：11月10号（周二）晚上07:30--08:30
地点：金融工程研究中心105
摘要：Paper I: 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.
     Paper II: In this paper, we separate the integrated volatility of an individual Ito process into the integrated systematic and idiosyncratic volatility, and estimate them by aggregation of local factor analysis with large dimensional high-frequency data. It is shown that, when both the sampling frequency $n$ and the dimensionality $p$ go to infinity, our estimators of the integrated systematic and idiosyncratic volatility are $sqrt{n}$ consistent, the best rate achieved in estimating the integrated volatility readily identified even with univariate high-frequency data. We also present an estimator of the integrated idiosyncratic volatility matrix under some sparsity assumption which typically does not hold for the integrated volatility matrix (the sum of the integrated systematic and idiosyncratic volatility matrices). It is proved that the estimator converges in the operator norm at the rate of $s_0(p)(frac{1}{sqrt{p}}+frac{sqrt{log{p}}}{k_n})^{1-q}$ where $s_0(p)$ is a measure of sparsity. Numerical studies including the Monte-Carlo experiments and real data analysis justify the performance of our estimators.
 
面向对象：13级金融数学本科生，13级统计学本科生，金融中心，统计中心研究生及相关老师。