Two-way Matrix Autoregressive Model with Thresholds

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.