Abstract: Time series analyses are often used to model a continuous response for all individuals at equally spaced time points. With the rapid advance of social network sites, network data are becoming increasingly available. The network vector autoregression (NAR) model incorporates the network information among individuals. The response of each individual can be explained by its lagged value, the average of its neighbors, and a set of node-specific covariates. However, all individuals are assumed to be homogeneous because they share the same autoregression coef- ficients. To express individual heterogeneity, we develop a grouped NAR (GNAR) model. Individuals in a network can be classified into different groups characterized by sets of parameters. The strict stationarity of the GNAR model is established. Two estimation procedures are developed, as well as the asymptotic properties of the proposed model. Numerical studies are conducted to evaluate the finite-sample performance of our proposed methodology. Lastly, two real-data examples are presented, based on studies on user posting behavior on the Sina Weibo platform and on air pollution patterns (especially PM_2.5 ) in mainland China, respectively.

Key words and phrases: EM algorithm, network data, ordinary least square estimator, vector autoregression.