Two-way dynamic factor models for high-dimensional matrix-valued time series

In this article, we introduce a two-way dynamic factor model (2w-DFM) for high-dimensional matrix-valued time series and study some of the basic theoretical properties in terms of identifiability and estimation accuracy. The proposed model aims to capture separable and low-dimensional effects of row and column attributes and their correlations across rows, columns, and time points. Complementary to other dynamic factor models for high-dimensional data, the 2w-DFM inherits the dimension-reduction feature of factor models but assumes additive row and column factors for easier interpretability. We provide conditions to ensure model identifiability and consider a quasi-likelihood based two-step method for parameter estimation. Under an asymptotic regime where the size of the data matrices as well as the length of the time series increase, we establish that the estimators achieve the optimal rate of convergence and are asymptotically normal. The asymptotic properties are reaffirmed empirically through simulation studies. An application to air quality data in Chinese cities is given to illustrate the merit of the 2w-DFM.