Dynamic Factor Models with Infinite-Dimensional Factor Space: One-Sided Representations

Abstract. Factor model methods recently have become extremely popular in the theory andpractice of large panels of time series data. Those methods rely on various factor models whichall are particular cases of the Generalized Dynamic Factor Model (GDFM) introduced inForni, Hallin, Lippi and Reichlin (2000). That paper, however, relies on Brillinger's dynamicprincipal components. The corresponding estimators are two-sided filters whose performanceat the end of the observation period or for forecasting purposes is rather poor. No such problem arises with estimators based on standard principal components, which have beendominant in this literature. On the other hand, those estimators require the assumptionthat the space spanned by the factors has finite dimension. In the present paper, we arguethat such an assumption is extremely restrictive and potentially quite harmful. Elaboratingupon recent results by Anderson and Deistler (2008a, b) on singular stationary processes withrational spectrum, we obtain one-sided representations for the GDFM without assuming finitedimension of the factor space. Construction of the corresponding estimators is also brieflyoutlined. In a companion paper, we establish consistency and rates for such estimators, andprovide Monte Carlo results further motivating our approach.