Résumé : We provide the asymptotic distributional theory for the so-called General or Generalized Dynamic Factor Model (GDFM), laying the foundations for an inferential approach in the GDFM analysis of high-dimensional time series. Our results are exploiting the duality between common shocksand dynamic loadings under a random cross-section approach to derive the asymptotic distribution of a class of estimators for common shocks, dynamic loadings, common components, and impulse response functions. An empirical application aimed at the construction of a “core” inflation indicator for the U.S. economy is presented, empirically demonstrating the superiority of the GDFM-based indicator over the most commonly adopted approaches, outperforming, in particular, the one based on Principal Components.