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【预告】统计学院系列学术报告(2017年第2期) 发布时间:2017-03-17 浏览次数:

报告题目:Principal component analysis for second-order stationary vector time series

报告时间:2017317 15:00

报告地点:教二114

人: 常晋源,20097月毕业于北京师范大学数学科学学院,获理学学士学位;20137月毕业于北京大学光华管理学院,获经济学博士学位;20139月至20172月在墨尔本大学数学与统计学院任研究员;20173月开始全职在西南财经大学统计学院工作,并担任西南财大电子科大四川省统计局四川移动数据科学与商业智能联合实验室执行主任。2012年获得国际数理统计协会Laha Award2013年获得中国数学会钟家庆数学奖;2016年破格入选四川省千人计划专家,获聘四川省人民政府特聘专家。主要研究领域为:超高维数据分析、高频数据分析以及Bootstrap方法等。过去五年,在统计学与计量经济学国际顶级期刊Annals of StatisticsBiometricsBiometrika以及Journal of Econometrics上发表论文十余篇。

报告摘要:We extend the principal component analysis (PCA) to secondorder stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a p-variate time series such that the transformed series is segmented into several lowerdimensional subseries, and those subseries are uncorrelated with each other both contemporaneously and serially. Therefore those lowerdimensional series can be analysed separately as far as the linear dynamic structure is concerned. Technically it boils down to an eigenanalysis for a positive definite matrix. When p is large, an additional step is required to perform a permutation in terms of either maximum cross-correlations or FDR based on multiple tests. The asymptotic theory is established for both fixed p and diverging p when the sample size n tends to infinity. Numerical experiments with both simulated and real data sets indicate that the proposed method is an effective initial step in analysing multiple time series data, which leads to substantial dimension reduction in modelling and forecasting high-dimensional linear dynamical structures. Unlike PCA for independent data, there is no guarantee that the required linear transformation exists. When it does not, the proposed method provides an approximate segmentation which leads to the advantages in, for example, forecasting for future values. The method can also be adapted to segment multiple volatility processes.

 




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