LAUSR

In the study of time series analysis, it is of great interest to model a continuous response for all the individuals at equally spaced time points. With the rapid advance of social network sites, network data are becoming increasingly available. In order to incorporate the network information among individuals, Zhu et al. (2017) developed a network vector autoregression (NAR) model. 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 the individuals are assumed to be homogeneous since they share the same autoregression coefficients. To express individual heterogeneity, we develop in this work a grouped NAR (GNAR) model. Individuals in a network can be classified into different groups, characterized by different sets of parameters. The strict stationarity of the GNAR model is established. Two estimation procedures are further developed as well as the asymptotic properties. Numerical studies are conducted to evaluate the finite sample performance of our proposed methodology. At last, two real data examples are presented for illustration purpose. They are the studies of user posting behavior on Sina Weibo platform and air pollution pattern (especially PM2.5) in mainland China.