报告人：孔新兵
报告地点：数学与统计学院415室
报告时间：2019年06月26日星期三15:00-16:00
邀请人：
报告摘要：
The global principal component analysis (GPCA), which means PCA is directly applied to the whole sample, is not reliable to reconstruct the common components of a large panel of high-frequency data when the factor loadings are time-varying, but it works when the factor loadings are constant. However, the local principal component analysis (LPCA) presented in Kong (2017) results in consistent estimates of the common components even if the factor loading processes follow It\^{o} semimartingales.
This motivates us to study the discrepancy between the GPCA and LPCA in recovering the common components of the large-panel high-frequency data. In this paper, we measure the discrepancy by the total sum of squared differences between common components reconstructed from GPCA and LPCA. We provide the asymptotic distribution of the discrepancy measure when the factor loadings are constant. Alternatively when some factor loadings are time-varying, the discrepancy measure explodes in a rate higher than $\sqrt{pk_n}$ under some mild conditions on the time-variation magnitude of the factor loadings where $k_n$ is the size of each subsample. We then apply the theory on testing the hypothesis that the factor loading matrix is a constant matrix. We show that the test performs well in controlling the type I error and detecting time-varying loadings. Our real data analysis provides evidence that the factor loading matrices are always time-varying.
主讲人简介：
孔新兵, 南京审计大学教授，研究兴趣为髙维数据分析和高频数据分析。主持国家自然科学基金项目2项，教育部人文社会科学项目一项。在统计学和计量经济学顶级发表论文十余篇。现为ISI推选会员，RMTA编委，担任现场统计学会多个分会常务理事和理事。曾入选江苏省双创博士计划，苏州市紧缺高层次人才引进计划。
