讲座主题：On the modelling and prediction of high-dimensional functional time series
嘉宾简介：常晋源，西南财经大学光华特聘教授、中国科学院数学与系统科学研究院研究员、博士生导师、数据科学与商业智能联合实验室执行主任、国家杰出青年科学基金获得者、四川省特聘专家、四川省统计专家咨询委员会委员。常晋源老师的研究兴趣主要集中在“超高维数据分析”和“高频金融数据分析”两个领域。常晋源老师的研究论文发表于Journal of Econometrics，Biometrika，Biometrics，The Annals of Statistics，Journal of the American Statistical Association，Journal of Business & Economic Statistics等统计学和计量学国际顶尖杂志。常晋源老师曾担任Journal of the Royal Statistical Society SeriesB副主编，现担任Journal of the AmericanStatistical Association、Journal of Business & Economic Statistics以及Statistica Sinica的副主编。
内容摘要：We propose a two-step procedure to model and predict high-dimensional functional time series, where the number of function-valued time series p is large in relation to the length of time series n. Our first step performs an eigenanalysis of a positive definite matrix, which leads to a one-to-one linear transformation for the original high-dimensional functional time series, and the transformed series can be segmented into several groups such that any two series from any two different groups are uncorrelatedboth contemporaneously and serially. Consequently in our second step those groups are handled separately without the information loss on the overall linear dynamic structure. The second step is devoted to establishing a finite-dimensional dynamical structure for all the functional time series within each group. Furthermore the finite-dimensional structure is represented by that of a vector time series. Modelling and forecasting for the original high-dimensional functional time series are realized via those for the vector time series in all the groups. We investigate the theoretical properties of our proposed methods, and illustrate the finite-sample performance through both extensive simulations and three real datasets.