A Random Graph-based Autoregressive Model for Networked Time Series

TL;DR

This paper introduces a flexible autoregressive model for networked time series data that effectively captures both influence and homophily, with a novel estimation method that requires minimal model specification and is supported by theoretical guarantees and empirical validation.

Contribution

It proposes a new autoregressive model with a flexible latent variable component for homophily and develops a differencing and neighbor smoothing estimation approach that relaxes model assumptions.

Findings

Estimation method is consistent and asymptotically normal.

Model accurately captures influence and homophily effects.

Method performs well in simulations and real social media data.

Abstract

Contemporary time series data often feature objects connected by a social network that naturally induces temporal dependence involving connected neighbours. The network vector autoregressive model is useful for describing the influence of linked neighbours, while recent generalizations aim to separate influence and homophily. Existing approaches, however, require either correct specification of a time series model or accurate estimation of a network model or both, and rely exclusively on least-squares for parameter estimation. This paper proposes a new autoregressive model incorporating a flexible form for latent variables used to depict homophily. We develop a first-order differencing method for the estimation of influence requiring only the influence part of the model to be correctly specified. When the part including homophily is correctly specified admitting a semiparametric form, we leverage and generalize the recent notion of neighbour smoothing for parameter estimation, bypassing the need to specify the generative mechanism of the network. We develop new theory to show that all the estimated parameters are consistent and asymptotically normal. The efficacy of our approach is confirmed via extensive simulations and an analysis of a social media dataset.