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

TL;DR

This paper introduces a comprehensive framework for inferring large-scale, time-varying, and lagged correlation networks from non-stationary multivariate time series with complex trends, using novel statistical testing and estimation techniques.

Contribution

It develops a unified multiple-testing procedure, difference-based estimators, and bootstrap methods to accurately recover dynamic network structures in complex non-stationary data.

Findings

Accurately detects time-varying network structures in simulations.

Effectively controls family-wise error rates with bootstrap.

Demonstrates practical applicability in empirical data analysis.

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.