Dynamic Factor Models with Innite-Dimensional Factor Space:Asymptotic Analysis

Factor models, all particular cases of the Generalized Dynamic Factor Model
(GDFM) introduced in Forni, Hallin, Lippi and Reichlin (2000), have become extremely
popular in the theory and practice of large panels of time series data. The asymptotic properties (consistency and rates) of the corresponding estimators have been studied in Forni,
Hallin, Lippi and Reichlin (2004). Those estimators, however, rely on Brillinger’s dynamic
principal components, and thus involve two-sided filters, which leads to rather poor forecasting performances. No such problem arises with estimators based on standard (static)
principal components, which have been dominant in this literature. On the other hand, the
consistency of those static estimators requires the assumption that the space spanned by the
factors has finite dimension, which severely restricts the generality afforded by the GDFM.
This paper derives the asymptotic properties of a semiparametric estimator of the loadings
and common shocks based on one-sided filters recently proposed by Forni, Hallin, Lippi and
Zaffaroni (2015). Consistency and exact rates of convergence are obtained for this estimator,
under a general class of GDFMs that does not require a finite-dimensional factor space. A
Monte Carlo experiment and an empirical exercise on US macroeconomic data corroborate
those theoretical results and demonstrate the excellent performance of those estimators in
out-of-sample forecasting.