One - Sided Representations of Generalized Dynamic Factor Models by Mario Forni ( University of Modena and Reggio Emilia )

In the present paper we study a semiparametric version of the Generalized Dynamic Factor Model introduced in Forni, Hallin, Lippi and Reichlin (2000). Precisely, we suppose that the common components have rational spectral density, while no parametric structure is assumed for the idiosyncratic components. The parametric structure assumed for the common components does not imply that the model has a static representation (though the converse implication holds), a strong restriction which is shared by most of the literature on large-dimensional dynamic factor models. We use recent results on singular stationary processes with rational spectral density, to obtain a finite autoregressive representation for the common components. We construct an estimator for the model parameters and the common shocks. Consistency and rates of convergence are obtained. An empirical section, based on US macroeconomic time series, compares estimates based on our model with those based on the usual staticrepresentation restriction. We find convincing evidence that the latter is not supported by the data. JEL subject classification : C0, C01, E0.