Forecasting Dynamic Factor Scores by UNALSE Spectral Density Matrix Estimator

In this short paper, we propose a new generalized dynamic factor model estimator using the UNALSE spectral density matrix estimator, which is obtained by nuclear norm plus ℓ1 norm penalization. In this way, the matrix of factor loadings is optimally estimated in the minmax sense, as are the factor scores by both Bartlett’s and Thomson’s method. This approach makes it possible to counteract the impossibility of obtaining the same estimates with classical dynamic principal component analysis, due to the fact that the estimated idiosyncratic covariance matrix is not invertible. The theoretical background is presented and mathematical results are announced to demonstrate the usefulness and novelty of the new approach. In particular, the optimality properties of the new estimates of factor loadings and scores are highlighted.