Recently, the paper “Statistical Inference for High-Dimensional Spectral Density Matrix”, jointly completed by Professor Jinyuan Chang, Associate Researcher Qing Jiang of Beijing Normal University at Zhuhai, senior statistical analyst Tucker McElroy from the U.S. Census Bureau, and Professor Xiaofeng Shao from Washington University in St. Louis has been officially accepted by Journal of the American Statistical Association.
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.
Author Introduction
Jinyuan Chang, executive director of the Joint Laboratory of Data Science and Business Intelligence at Southwestern University of Finance and Economics, Guanghua distinguished professor, and recipient of the National Science Fund for Distinguished Young Scholars of China. Mainly engaged in two research fields: ultra-high dimensional data analysis and high-frequency financial data analysis.
Qing Jiang, associate researcher of Beijing Normal University at Zhuhai, primarily engaged in research in the fields of high-dimensional data analysis and model testing.
Tucker McElroy, senior statistical analyst at the U.S. Census Bureau, mainly focusing on research in time series analysis and signal extraction.
Xiaofeng Shao, professor at Washington University in St. Louis, primarily involved in research areas such as time series analysis, high-dimensional data analysis, and functional data analysis.
