报 告 人：常晋源 教授

报告题目：Statistical Inference for High-Dimensional Spectral Density Matrix

报告时间：2023年10月14日（周六上午11：10 )

报告地点：太阳集团官方网站入口学术报告厅（静远楼1506室）

主办单位：数学研究院、太阳集团官方网站入口、科学技术研究院

报告人简介：

       常晋源，西南财经大学光华特聘教授、中科院数学与系统科学研究院研究员，主要从事“超高维数据分析”和“高频金融数据分析”相关的工作，正担任Journal of the American Statistical Association, Journal of Business & Economic Statistics以及Statistica Sinica的Associate Editor。

报告摘要：

       The spectral density matrix is a fundamental object of interest in time series analysis, and it encodes both contemporary and dynamic linear relationships between component processes of the multivariate system. In this paper we develop novel inference procedures for the spectral density matrix in the high-dimensional setting. Specifically, we introduce a new global testing procedure to test the nullity of the cross-spectral density for a given set of frequencies and across pairs of component indices. For the first time, both Gaussian approximation and parametric bootstrap methodologies are employed to conduct inference for a high-dimensional parameter formulated in the frequency domain, and new technical tools are developed to provide asymptotic guarantees of the size accuracy and power for global testing. We further propose a multiple testing procedure for simultaneously testing the nullity of the cross-spectral density at a given set of frequencies. The method is shown to control the false discovery rate. Both numerical simulations and a real data illustration demonstrate the usefulness of the proposed testing methods.