Determining the Number of Factors in Two-way Factor Model of High-dimensional Matrix-variate Time Series: a White-noise Based Method for Serial Correlation Models

This study proposes a novel two-way factor modeling framework for high-dimensional matrixvariate time series.Motivated by the objective of identifying white noise components, we develop two ratio-based estimators leveraging the element-wise maximum norm and Frobenius norm of sample autocovariance matrices to determine the dimensions of row and column factor spaces.To reduce the impact of cross-row and cross-column factor strength heterogeneity, the original matrix factor model is reparameterized as a reduced-form model containing only a row loading matrix or a column loading matrix.We then investigate the refined ratio-based methods developed under this reparameterized framework.Under regularity conditions, we establish the theoretical properties of the proposed methods, demonstrating their consistency in estimating the number of factors.Through Monte Carlo simulations and a real data application, we validate the finite-sample performance of the proposed methods and compare them with existing alternatives.