Dynamic Factor Models, Cointegration, and Error Correction Mechanisms

Abstract

In this paper we study Dynamic Factor Models when the factors Ft are I(1) and singular, i.e. rank(Ft) < dim(Ft). By combining the classic Granger Representation Theorem with recent results by Anderson and Deistler on singular stochastic vectors, we prove that, for generic values of the parameters, Ft has an Error Correction representation with two unusual features: (i) the autoregressive matrix polynomial is finite, (ii) the number of error-terms is equal to the number of transitory shocks plus the dierence between the dimension and the rank of Ft. This result is the basis for the correct specification of an autoregressive model for Ft. Estimation of impulse-response functions is also discussed. Results of an empirical analysis on a US quarterly database support the use of our model.