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arXiv · 2302.05158

Time-varying correlation network analysis of non-stationary multivariate time series with complex trends

Lujia Bai·Weichi Wu
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Abstract

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.

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Lujia Bai, Weichi Wu. 2023-02-10. Time-varying correlation network analysis of non-stationary multivariate time series with complex trends. https://arxiv.org/abs/2302.05158

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