This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified multiple-testing procedure of time-lagged cross-correlation functions with a fixed or diverging number of lags, our method can accurately disclose flexible time-varying network structures associated with complex functional structures at all time points. We broaden the applicability of our method to the structure breaks by developing difference-based nonparametric estimators of cross-correlations, achieve accurate family-wise error control via a bootstrap-assisted procedure adaptive to the complex temporal dynamics, and enhance the probability of recovering the time-varying network structures using a new uniform variance reduction technique. We prove the asymptotic validity of the proposed method and demonstrate its effectiveness in finite samples through simulation studies and empirical applications.

翻译：本文提出了一种灵活的框架，用于从具有分段平滑趋势的多元或高维非平稳时间序列中推断大规模时变与时滞相关网络。该方法基于一种新颖且统一的多重检验程序（针对固定或发散滞后数量的时滞互相关函数），能够精确揭示所有时间点上与复杂函数结构相关的灵活时变网络结构。通过开发基于差分的互相关非参数估计器，我们将方法的适用性扩展到结构突变场景；采用自举辅助程序自适应复杂的时间动态特性，实现对族系误差的精确控制；并利用一种新的均匀方差缩减技术，提高恢复时变网络结构的概率。我们证明了所提方法的渐近有效性，并通过模拟研究和实证应用展示了其在有限样本中的有效性。