Statistical Inference for High-Dimensional Spectral Density Matrix
Holder： Jinyuan Chang (Southwestern University of Finance and Economics)
Location：Room 217, Guanghua Building 2
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.
About the Speaker:
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，主要研究兴趣包括“超高维数据分析”和“高频金融数据分析”两个领域，现担任Journal of the American Statistical Association、Journal of Business & Economic Statistics以及Statistica Sinica的副主编。
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