Uniform Variance Reduced Simultaneous Inference of Time-Varying Correlation Networks

This paper proposes a unified framework for inferring large-scale time-varying correlation networks via data-driven time-varying thresholds that can control uncertainty simultaneously. The framework allows the dimension of time series vectors to be fixed or diverging at a high polynomial rate of the sample size. It also allows the time series to exhibit changing temporal characteristics beyond stationarity without specific structural assumptions. Motivated by the practical issue that the confidence band of non-parametric estimators of correlations can exceed their natural domain [−1, 1] (see, for example [1])), we propose a simple uniform variance reduction technique. When applied to the construction of a correlation network, the new device yields more accurate thresholds, which enhance the probability of recovering the time-varying network structures. We broaden the applicability of our method by developing difference-based estimators of cross-correlations that are robust to structure breaks in the time-varying mean functions, and by allowing both a fixed and a diverging number of lags in the correlation functions. We prove the asymptotic validity of the proposed method, especially in achieving accurate family-wise error control when disclosing flexible time-varying network structures. The effectiveness of our method in finite samples is demonstrated through simulation studies and data analysis.