This paper considers an approximate dynamic matrix factor model that accounts for the time series nature of the data by explicitly modelling the time evolution of the factors. We study estimation of the model parameters based on the Expectation Maximization (EM) algorithm, implemented jointly with the Kalman smoother which gives estimates of the factors. We establish the consistency of the estimated loadings and factor matrices as the sample size $T$ and the matrix dimensions $p_1$ and $p_2$ diverge to infinity. We then extend this approach to: (a) the case of arbitrary patterns of missing data and (b) the presence of common stochastic trends. The finite sample properties of the estimators are assessed through a large simulation study and two applications on: (i) a financial dataset of volatility proxies and (ii) a macroeconomic dataset covering the main euro area countries.

翻译：本文研究一种近似动态矩阵因子模型，该模型通过显式建模因子的时间演化来考虑数据的时间序列特性。我们基于期望最大化（EM）算法研究模型参数的估计方法，该算法与卡尔曼平滑器联合实现以提供因子估计。我们证明了当样本量$T$及矩阵维度$p_1$和$p_2$趋于无穷时，估计的载荷矩阵和因子矩阵具有一致性。随后我们将该方法拓展至：（a）任意缺失数据模式的情形，以及（b）存在共同随机趋势的情形。通过大规模仿真研究及两个实证应用评估估计量的有限样本性质：（i）波动率代理指标的金融数据集，及（ii）涵盖欧元区主要国家的宏观经济数据集。