Large-scale matrix data has been widely discovered and continuously studied in various fields recently. Considering the multi-level factor structure and utilizing the matrix structure, we propose a multilevel matrix factor model with both global and local factors. The global factors can affect all matrix times series, whereas the local factors are only allow to affect within each specific matrix time series. The estimation procedures can consistently estimate the factor loadings and determine the number of factors. We establish the asymptotic properties of the estimators. The simulation is presented to illustrate the performance of the proposed estimation method. We utilize the model to analyze eight indicators across 200 stocks from ten distinct industries, demonstrating the empirical utility of our proposed approach.

翻译：大规模矩阵数据近年来在各个领域被广泛发现并持续研究。考虑到多级因子结构并利用矩阵结构，我们提出了一种包含全局因子和局部因子的多层矩阵因子模型。全局因子可以影响所有矩阵时间序列，而局部因子仅允许影响每个特定矩阵时间序列内部。估计过程能够一致地估计因子载荷并确定因子数量。我们建立了估计量的渐近性质。通过模拟实验展示了所提出估计方法的性能。我们利用该模型分析了来自十个不同行业、200只股票的八个指标，证明了我们提出方法的实证效用。