Statistical Inference for High-Dimensional Spectral Density Matrix

Speaker：Chang Jinyuan (Professor, School of Statistics, Southwestern University of Finance and Economics)

Host：Lin Jianhao, Professor, Lingnan College

Time and Date：14:30, Jun. 19, 2023

Venue: Wang Daohan Conference Room(101), Lingnan Hall

Language: English + Chinese

Abstract:

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.

Profile of the speaker:

CHANG Jinyuan, PhD in Economics, Professor, PhD supervisor

He has published 16 papers on top international journals such as Annals of Statistics, Biometrika, Journal of Econometrics, Biometrics etc., and he is associate editor of Journal of the Royal Statistical Society Series B, Statistica Sinica, Journal of Business & Economic Statistics. He is the Awardee of the 16th Fok Ying-Tong Education Foundation Funds for Young Teachers in the Higher Education Institutions of China in 2018, and he won the First Prize of the 17th Fok Ying-Tong Outstanding Young Teacher Award in the Higher Education Institutions of China in 2020.

Research Interests: High Dimensional Data Analysis, Empirical Likelihood and Its Application, Financial Econometrics, Network Data Analysis, Functional Data Analysis.