Split-and-Conquer: Distributed Factor Modeling for High-Dimensional Matrix-Variate Time Series

TL;DR

This paper introduces a distributed factor modeling framework for high-dimensional matrix-variate time series that improves computational efficiency and preserves data structure, with extensions to nonstationary data.

Contribution

A novel distributed approach using tensor PCA for high-dimensional matrix-variate time series that maintains data structure and extends to nonstationary cases.

Findings

Enhanced computational efficiency demonstrated in simulations

Accurate estimation of loading and factor matrices shown

Improved predictive performance in real data applications

Abstract

In this paper, we propose a distributed framework for reducing the dimensionality of high-dimensional, large-scale, heterogeneous matrix-variate time series data using a factor model. The data are first partitioned column-wise (or row-wise) and allocated to node servers, where each node estimates the row (or column) loading matrix via two-dimensional tensor PCA. These local estimates are then transmitted to a central server and aggregated, followed by a final PCA step to obtain the global row (or column) loading matrix estimator. Given the estimated loading matrices, the corresponding factor matrices are subsequently computed. Unlike existing distributed approaches, our framework preserves the latent matrix structure, thereby improving computational efficiency and enhancing information utilization. We also discuss row- and column-wise clustering procedures for settings in which the group memberships are unknown. Furthermore, we extend the analysis to unit-root nonstationary matrix-variate time series. Asymptotic properties of the proposed method are derived for the diverging dimension of the data in each computing unit and the sample size $T$. Simulation results assess the computational efficiency and estimation accuracy of the proposed framework, and real data applications further validate its predictive performance.