FNETS: Factor-adjusted network estimation and forecasting for high-dimensional time series

TL;DR

FNETS is a comprehensive methodology for estimating and forecasting networks in high-dimensional time series by combining factor adjustment, sparse VAR modeling, and network inference, with proven consistency and good empirical performance.

Contribution

The paper introduces FNETS, a novel approach that integrates factor adjustment with sparse VAR modeling for network estimation and forecasting in high-dimensional time series.

Findings

FNETS accurately estimates multiple types of networks underlying the data.

The method achieves uniform consistency in network estimation and forecasting.

Simulation and real data studies demonstrate FNETS's effectiveness.

Abstract

We propose FNETS, a methodology for network estimation and forecasting of high-dimensional time series exhibiting strong serial- and cross-sectional correlations. We operate under a factor-adjusted vector autoregressive (VAR) model which, after accounting for pervasive co-movements of the variables by {\it common} factors, models the remaining {\it idiosyncratic} dynamic dependence between the variables as a sparse VAR process. Network estimation of FNETS consists of three steps: (i) factor-adjustment via dynamic principal component analysis, (ii) estimation of the latent VAR process via $\ell_1$-regularised Yule-Walker estimator, and (iii) estimation of partial correlation and long-run partial correlation matrices. In doing so, we learn three networks underpinning the VAR process, namely a directed network representing the Granger causal linkages between the variables, an undirected one embedding their contemporaneous relationships and finally, an undirected network that summarises both lead-lag and contemporaneous linkages. In addition, FNETS provides a suite of methods for forecasting the factor-driven and the idiosyncratic VAR processes. Under general conditions permitting tails heavier than the Gaussian one, we derive uniform consistency rates for the estimators in both network estimation and forecasting, which hold as the dimension of the panel and the sample size diverge. Simulation studies and real data application confirm the good performance of FNETS.