Two-way Matrix Autoregressive Model with Thresholds

TL;DR

This paper introduces a novel two-way matrix autoregressive model with thresholds that allows for different threshold variables for rows and columns, improving model flexibility and performance in matrix-valued time series analysis.

Contribution

It develops a comprehensive methodology for the 2-MART model, addressing challenges of using two different threshold variables, and demonstrates advantages over existing models.

Findings

Greater dimension reduction achieved

Improved model fitting and prediction accuracy

More plausible interpretations of matrix time series

Abstract

Recently, matrix-valued time series data have attracted significant attention in the literature with the recognition of threshold nonlinearity representing a significant advance. However, given the fact that a matrix is a two-array structure, it is unfortunate, perhaps even unusual, for the threshold literature to focus on using the same threshold variable for the rows and the columns. In fact, evidence in economic, financial, environmental and other data shows advantages of allowing the possibilities of two different threshold variables (with possibly different threshold parameters for rows and columns), hence the need for a Two-way Matrix AutoRegressive model with Thresholds (2-MART). Naturally, two threshold variables pose new and perhaps even fierce challenges, which might be the reason behind the adoption of only one threshold variable in the literature up to now. In this paper, we develop a comprehensive methodology for the 2-MART model, by overcoming various challenges. Compared with existing models in the literature, the new model can achieve greater dimension reduction, much better model fitting, more accurate predictions, and more plausible interpretations.