Estimation of dynamic networks for high-dimensional nonstationary time series

TL;DR

This paper introduces a two-step method for estimating high-dimensional, nonstationary time-varying networks that captures both abrupt and smooth changes, with proven consistency and application to financial data.

Contribution

It proposes a novel combined approach for detecting change points and estimating time-varying networks in high-dimensional nonstationary time series.

Findings

Method accurately detects change points and network structures.

Theoretical convergence rates are established under mild conditions.

Applied to S&P 500 data, revealing dynamic market network changes.

Abstract

This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To simultaneously handle these two types of time-varying features, a two-step approach is proposed: multiple change point locations are first identified based on comparing the difference between the localized averages on sample covariance matrices, and then graph supports are recovered based on a kernelized time-varying constrained $L_1$-minimization for inverse matrix estimation (CLIME) estimator on each segment. We derive the rates of convergence for estimating the change points and precision matrices under mild moment and dependence conditions. In particular, we show that this two-step approach is consistent in estimating the change points and the piecewise smooth precision matrix function, under certain high-dimensional scaling limit. The method is applied to the analysis of network structure of the S\&P 500 index between 2003 and 2008.