A General Modeling Framework for Network Autoregressive Processes

ABSTRACT

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

KEYWORDS:

• Inference
• Misspecified network connectivity
• Network autoregressive process
• Ridge penalty
• Stability

Supplementary Materials

The PDF file contains proofs of all Theorems, additional lemmas and other technical material not included in the main file due to space considerations, as well as additional simulation results, tables and figures. The HTML files contain R code to reproduce Tables 4, 1 and part of Table 2, as well as the comparisons in Section F.1.

Acknowledgments

The authors would like to thank the Editor, Associate Editor, and anonymous reviewers for many constructive comments and suggestions.

Notes

1 https://www.ncdc.noaa.gov/

Additional information

Funding

The work of GM and AS was supported in part by NSF grant DMS 2124507.