Maximum likelihood estimation of dynamic factor models using general cross sectional covariance

This thesis introduces a novel maximum likelihood approach to econometric estimation of Dynamic Factor Models (DFMs). The main novelty is the relaxation of the assumption that the cross sectional covariance matrix is diagonal, which is predominant in existing estimation approaches. The approach should therefore be more efficient than existing approaches in finite samples with a significant degree of cross sectional error correlation. I refer to the approach as the General Covariance DFM, or GCDFM. The cross sectional and dynamic coefficients are concentrated out as functions of the factors using maximum likelihood formulae. Importantly, this allows concentrating out the cross sectional covariance matrix. The approach is implemented using numerical optimisation of the concentrated log-likelihood. An analytical implementation is also introduced by solving the first order conditions with respect to the factors. The GCDFM is demonstrated in an out of sample forecasting exercise in a Monte Carlo simulation setting and a standard large macroeconomic data set. The results are positive for the GCDFM, which for the large macroeconomic data set indicates that the assumption of diagonal cross sectional covariance matrix is likely invalid. Lastly, the approach is extended to GARCH modelling of the dynamic factor errors in a second stage for use in equities portfolio optimisation. The GCDFM is shown to work well across 5 large equities data sets, with higher out of sample Sharpe ratios overall compared to other DFM estimation approaches. This indicates that the predominant diagonal cross sectional covariance assumption in DFMs may be inappropriate in an equities portfolio optimisation context, once GARCH effects have been accounted for.