Community network auto-regression for high-dimensional time series

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