報 告 人：常晉源 教授

報告題目：Statistical Inference for High-Dimensional Spectral Density Matrix

報告時間：2023年10月14日（周六上午11：10 )

報告地點：江蘇師范大學數學與統計學院學術報告廳（靜遠樓1506室）

主辦單位：數學研究院、數學與統計學院、科學技術研究院

報告人簡介：

       常晉源，西南財經大學光華特聘教授、中科院數學與系統科學研究院研究員，主要從事“超高維數據分析”和“高頻金融數據分析”相關的工作，正擔任Journal of the American Statistical Association, Journal of Business & Economic Statistics以及Statistica Sinica的Associate Editor。

報告摘要：

       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.