An analytical approach to estimating dynamic factor models with macroeconomic application

Until recently literature on dynamic factor models invariably assumed that the cross sectional error covariance matrix is diagonal. This is due to the many parameters which need to be estimated for large data sets, which is known as the curse of dimensionality. Spencer (2024) introduced a novel approach which relaxes the diagonal assumption. This is achieved by concentrating out the parameters with the coefficients being based on maximum likelihood estimates. Importantly, the cross sectional covariance matrix is concentrated out so does not need to be explicitly estimated. The approach was implemented by numerical optimisation. Out of sample tests using Monte Carlo simulations showed the general covariance approach to perform well, with smaller prediction errors overall compared to a range of existing diagonal approaches and a diagonal equivalent of the general covariance approach. The present paper introduces an analytical implementation of the general covariance approach which avoids the need for numerical optimisation. The factors are instead estimated by solving the first order conditions with respect to the factors. The approaches are demonstrated on a large macroeconomic data set so the results and methodology should therefore be of interest to macro-economists and policy makers. The results are positive for the general covariance approaches, which indicates that the assumption of diagonal cross sectional covariance matrix is likely invalid for the large macroeconomic data set.