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 Quasi Maximum Likelihood estimation of the model parameters based on the Expectation Maximization (EM) algorithm, implemented jointly with the Kalman smoother which gives estimates of the factors. This approach allows to easily handle arbitrary patterns of missing data. 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. The finite sample properties of the estimators are assessed through a large simulation study and an application to a financial dataset of volatility proxies.

翻译：本文研究一种近似动态矩阵因子模型，该模型通过对因子时间演化的显式建模来考虑数据的时间序列特性。我们基于期望最大化（EM）算法研究了模型参数的拟极大似然估计，该方法与卡尔曼平滑器联合实现以获取因子估计值。此方法能够轻松处理任意模式的缺失数据。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，估计的载荷矩阵与因子矩阵具有一致性。通过大规模模拟研究及对波动率代理金融数据集的应用，评估了估计量的有限样本性质。