The general dynamic factor model: One-sided representation results

Recent dynamic factor models have been almost exclusively developed under the assumption that the common components span a finite-dimensional vector space. However, this finite-dimension assumption rules out very simple factor-loading patterns and is therefore severely restrictive. The general case has been studied, using a frequency domain approach, in Forni, Hallin, Lippi and Reichlin (2000). That paper produces an estimator of the common components that is consistent but is based on filters that are two-sided and therefore unsuitable for prediction. The present paper, assuming a rational spectral density for the common components, obtains a one-sidedestimator without the finite-dimension assumption.