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.

翻译：本文提出了一种系统框架，用于在从高维、非线性、非高斯且非平稳的时间序列中学习时变相关网络时控制错误发现率，这些时间序列具有递增的潜在均值突变点数量。我们提出了一种基于自助法的辅助方法，从对突变点不敏感的时变相关函数的稳健估计中推导出依赖且时变的p值。我们的方法基于一种新的高维高斯近似结果，用于实现跨时间和不同坐标的p值均匀近似。此外，我们为依赖且时变的p值建立了理论保证的Benjamini–Hochberg和Benjamini–Yekutieli程序，能够实现均匀的错误发现率控制。所提出的方法得到了严格的数学证明和模拟研究的支持。我们还通过脑电图和金融时间序列数据展示了该框架在现实世界中的应用。