A General Modeling Framework for Network Autoregressive Processes

A general flexible framework for Network Autoregressive Processes (NAR) is developed, wherein the response of each node in network linearly depends on its past values, a prespecified linear combination neighboring nodes and set node-specific covariates. The corresponding coefficients are node-specific, can accommodate heavier than Gaussian errors with spatial-autoregressive, factor-based, or certain settings covariance structures. We provide sufficient condition that ensures stability (stationarity) underlying NAR significantly weaker counterparts previous work literature. Further, we develop ordinary (estimated) generalized least squares estimators both fixed, as well diverging numbers nodes, also their ridge regularized exhibit better performance large settings, together asymptotic distributions. derive distributions be used testing various hypotheses interest to practitioners. address issue misspecifying connectivity impact aforementioned parameter estimators. illustrated synthetic real air pollution data.