Dynamic Matrix Factor Models for High Dimensional Time Series

TL;DR

This paper introduces a dynamic matrix factor model with autoregressive structure for high-dimensional matrix time series, enabling better prediction and understanding of their underlying dynamics.

Contribution

It extends standard matrix factor models by incorporating a matrix autoregressive component, allowing for prediction and dynamic analysis of high-dimensional data.

Findings

The proposed model effectively captures the dynamics of matrix time series.

Simulation studies demonstrate the estimation procedures' accuracy.

Application to NYC taxi data shows practical usefulness.

Abstract

Matrix time series, which consist of matrix-valued data observed over time, are prevalent in various fields such as economics, finance, and engineering. Such matrix time series data are often observed in high dimensions. Matrix factor models are employed to reduce the dimensionality of such data, but they lack the capability to make predictions without specified dynamics in the latent factor process. To address this issue, we propose a two-component dynamic matrix factor model that extends the standard matrix factor model by incorporating a matrix autoregressive structure for the low-dimensional latent factor process. This two-component model injects prediction capability to the matrix factor model and provides deeper insights into the dynamics of high-dimensional matrix time series. We present the estimation procedures of the model and their theoretical properties, as well as empirical analysis of the estimation procedures via simulations, and a case study of New York city taxi data, demonstrating the performance and usefulness of the model.