On the Existence of One‐Sided Representations for the Generalised Dynamic Factor Model

ABSTRACT We study the Generalised Dynamic Factor Model (GDFM) and show that the dynamic common component, that is, the common component of the GDFM, can be expressed using only current and past observations under mild assumptions. Specifically, we require (i) the dynamic common component to be purely non‐deterministic and (ii) the exclusion of pathological non‐fundamentalness in its transfer‐function. This generalises earlier works on the one‐sidedness problem—previously established in VAR(MA) frameworks—and demonstrates that the GDFM's apparent two‐sidedness is purely a choice of representation and not a structural feature. Moreover, the dynamic common component admits a clear economic interpretation: it is the projection of observed variables onto the infinite past of the economy's common shocks. Consequently, impulse‐response analysis in factor models should be based on the dynamic rather than the static decomposition, as the latter captures only the contemporaneous co‐movement.