Learning Time-Varying Correlation Networks with FDR Control via Time-Varying P-values

This paper presents a systematic framework for controlling false discovery rate in learning time-varying correlation networks from high-dimensional, non-linear, non-Gaussian and non-stationary time series with an increasing number of potential abrupt change points in means. We propose a bootstrap-assisted approach to derive dependent and time-varying P-values from a robust estimate of time-varying correlation functions, which are not sensitive to change points. Our procedure is based on a new high-dimensional Gaussian approximation result for the uniform approximation of P-values across time and different coordinates. Moreover, we establish theoretically guaranteed Benjamini--Hochberg and Benjamini--Yekutieli procedures for the dependent and time-varying P-values, which can achieve uniform false discovery rate control. The proposed methods are supported by rigorous mathematical proofs and simulation studies. We also illustrate the real-world application of our framework using both brain electroencephalogram and financial time series data.