Network Autoregression for Incomplete Matrix-Valued Time Series

TL;DR

This paper introduces a novel matrix network autoregression model for analyzing incomplete matrix-valued time series with network structures, incorporating covariates and low-rank matrices, and provides theoretical guarantees and practical applications.

Contribution

It proposes a new model for matrix time series with network data, including a two-step estimation, bias correction, and theoretical analysis of estimators.

Findings

Effective estimation of network autoregression coefficients.

Bias reduction improves estimator accuracy.

Successful application to Yelp data analysis.

Abstract

We study the dynamics of matrix-valued time series with observed network structures by proposing a matrix network autoregression model with row and column networks of the subjects. We incorporate covariate information and a low rank intercept matrix. We allow incomplete observations in the matrices and the missing mechanism can be covariate dependent. To estimate the model, a two-step estimation procedure is proposed. The first step aims to estimate the network autoregression coefficients, and the second step aims to estimate the regression parameters, which are matrices themselves. Theoretically, we first separately establish the asymptotic properties of the autoregression coefficients and the error bounds of the regression parameters. Subsequently, a bias reduction procedure is proposed to reduce the asymptotic bias and the theoretical property of the debiased estimator is studied. Lastly, we illustrate the usefulness of the proposed method through a number of numerical studies and an analysis of a Yelp data set.