A note on generalized factor analysis models

An interesting generalization of dynamic factor analysis models has been proposed recently by Forni, Lippi and collaborators. These models, called generalized dynamic factor analysis models describe observations of infinite cross-sectional dimension. Quite surprisingly the inherent non-uniqueness of factor analysis models does not occur in this generalized context. We attempt an explanation of this fact by restricting the analysis to static generalized factor models. We show that there is a natural interpretation of generalized factor analysis models in terms of Wold decomposition of stationary sequences. A stationary sequence admits a (unique) generalized factor analysis decomposition if and only if two rather natural conditions are satisfied.