Community Network Auto-Regression for High-Dimensional Time Series

Abstract

Modeling responses on the nodes of a large-scale network is an important task that arises commonly in practice. This paper proposes a community network vector autoregressive (CNAR) model, which utilizes the network structure to characterize the dependence and intra-community homogeneity of the high dimensional time series. The CNAR model greatly increases the flexibility and generality of the network vector autoregressive (Zhu et al., 2017, NAR) model by allowing heterogeneous network effects across different network communities. In addition, the non-community-related latent factors are included to account for unknown cross-sectional dependence. The number of network communities can diverge as the network expands, which leads to estimating a diverging number of model parameters. We obtain a set of stationary conditions and develop an efficient two-step weighted least-squares estimator. The consistency and asymptotic normality properties of the estimators are established. The theoretical results show that the two-step estimator improves the one-step estimator by an order of magnitude when the error admits a factor structure. The advantages of the CNAR model are further illustrated on a variety of synthetic and real datasets.

Autoregressive Networks

“…The literature on change-point detection in dynamic networks include Yang et al (2011); Wang et al (2018); Wilson et al (2019); Zhao et al (2019); Bhattacharjee et al (2020); Zhu et al (2020a). While autoregressive models have been used in dynamic networks for modelling continuous responses observed from nodes (Zhu et al, 2017(Zhu et al, , 2019Chen et al, 2020;Zhu et al, 2020b), to our best knowledge no attempts have been made on modelling the dynamics of adjacency matrices in an autoregressive manner. Kang et al (2017) uses dynamic network as a tool to model non-stationary vector autoregressive processes.…”

Factor Network Autoregressions

“…Our approach is especially related to the NAR model by Zhu et al (2017) and the community network autoregression (CNAR) by Chen et al (2020a). Specifically, Zhu et al (2017) develop a VAR model in which the dynamics depends on the structure of a network.…”

“…Specifically, Zhu et al (2017) develop a VAR model in which the dynamics depends on the structure of a network. Chen et al (2020a) extend this approach by allowing for heterogeneous network effects across different network communities and cross-sectional dependence of errors through a latent factor structure.…”

Network Influence with Latent Homophily and Measurement Error

“…The Spatial autoregression model (SAR) [57], originally developed for spatial data analysis has been adopted for estimating network influence both when a single time point measurement of the network and outcome is available as well as in the longitudinal settings [7,43,47,44,42,35,89,45]. Recently the network autoregressive model (NAR) [89] and extensions of it [14,88,87,85], have been proposed as tools for modeling and predicting networked time series. Such models are closely related to the longitudinal version of the SAR models where both the outcome and the network are observed over multiple time points.…”