Embedding Network Autoregression for time series analysis and causal peer effect inference

Music City Center 

We propose an Embedding Network Autoregressive Model (ENAR) for multivariate networked longitudinal data. We assume the network is generated from a latent variable model, and these unobserved variables are included in a structural peer effect model or a time series network autoregressive model as additive effects. This approach takes a unified view of two related yet fundamentally different problems: (1) modeling and predicting multivariate networked time series data and (2) causal peer influence estimation in the presence of homophily from finite time longitudinal data. We show that the estimated momentum and peer effect parameters are consistent and asymptotically normally distributed in asymptotic setups with a growing number of network vertices N while including growing time points T (time series) and finite T (peer effect) cases. Our theoretical results encompass cases when the network is modeled with the RDPG model and a more general latent space model. We also develop selection criteria when the number of latent variables K is unknown that provably does not under-select and show that the theoretical guarantees hold with the selected number for K as well.

Network peer effect

Network time series

Social influence

Latent homophily

Network embedding

Social network 

Section on Statistical Learning and Data Science