Estimation of large approximate dynamic matrix factor models based on the EM algorithm and Kalman filtering

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 and the matrix dimensions and diverge to infinity. 

We then illustrate two immediate extensions of this approach to: 

1. The case of arbitrary patterns of missing data and
2. The presence of common stochastic trends. The finite sample properties of the estimators are assessed through a large simulation study and two applications on:
   1. a financial dataset of volatility proxies
   2. a macroeconomic dataset covering the main euro area countries.