Matrix-valued Network Autoregression Model with Latent Group Structure

TL;DR

This paper introduces a novel group matrix network autoregression model for high-dimensional matrix-valued time series data, incorporating latent group structures to improve modeling and clustering.

Contribution

It proposes the GMNAR model with an iterative estimation algorithm and provides theoretical guarantees for consistent estimation of group memberships and parameters.

Findings

Successfully models network effects in matrix time series data.

Consistently estimates group memberships and model parameters.

Demonstrates practical utility on Yelp dataset.

Abstract

Matrix-valued time series data are frequently observed in a broad range of areas and have attracted great attention recently. In this work, we model network effects for high dimensional matrix-valued time series data in a matrix autoregression framework. To characterize the potential heterogeneity of the subjects and handle the high dimensionality simultaneously, we assume that each subject has a latent group label, which enables us to cluster the subject into the corresponding row and column groups. We propose a group matrix network autoregression (GMNAR) model, which assumes that the subjects in the same group share the same set of model parameters. To estimate the model, we develop an iterative algorithm. Theoretically, we show that the group-wise parameters and group memberships can be consistently estimated when the group numbers are correctly or possibly over-specified. An information criterion for group number estimation is also provided to consistently select the group numbers. Lastly, we implement the method on a Yelp dataset to illustrate the usefulness of the method.