A Markov-switching dynamic matrix factor model for the high-dimensional matrix time series

TL;DR

This paper introduces a Markov-switching dynamic matrix factor model for high-dimensional matrix time series, enabling structural interpretation and prediction with validated estimation methods and application to international trade networks.

Contribution

The paper develops a novel Ms-DMF model with an EM algorithm for joint parameter estimation, providing a new tool for analyzing complex matrix time series data.

Findings

Successfully estimates parameters with proven consistency and convergence.

Identifies key trade centers and cycles in international trade data.

Enhances understanding of trade network dynamics.

Abstract

In this study, we propose a novel model called the Markov-switching dynamic matrix factor (Ms-DMF) model, which serves the dual purpose of structural interpretation and prediction for high-dimensional matrix time series. When estimating the parameters of the Ms-DMF model, an EM (expectation maximization) algorithm was used to get a quasi-maximum likelihood estimation, where all the parameters are estimated jointly. A filtering and smoothing algorithm is used to compute the posterior expectations corresponding to the latent regimes and factors. The consistency, convergence rates, and limit distributions of the estimated parameters are established under mild conditions. The effectiveness of this estimation method is also validated by rigorous numerical simulations. Furthermore, we apply the Ms-DMF model to an international trade flow network. Compared to existing matrix factor models, our approach not only identifies the main import and export centers, but also recognizes the trade cycles between these centers. This provides profound insights and analytical capabilities to advance research in the field of international trade.