Modewise Additive Factor Model for Matrix Time Series

This paper introduces a novel Modewise Additive Factor Model (MAFM) for matrix-valued time series, offering a more flexible approach than existing multiplicative factor models like Tucker and CP. The key innovation lies in its additive structure, allowing for separate modeling of row-specific and column-specific latent effects. The paper's contribution is significant because it provides a computationally efficient estimation procedure (MINE and COMPAS) and a data-driven inference framework, including convergence rates, asymptotic distributions, and consistent covariance estimators. The development of matrix Bernstein inequalities for quadratic forms of dependent matrix time series is a valuable technical contribution. The paper's focus on matrix time series analysis is relevant to various fields, including finance, signal processing, and recommendation systems.