A Distributed Lag Approach to the Generalised Dynamic Factor Model

Abstract

We propose a simple estimator for the dynamic decomposition of the Generalized Dynamic Factor Model that avoids frequency-domain methods. First, we show that it is a reasonable approximation to assume that the dynamic common component of the Generalized Dynamic Factor Model admits a representation in terms of current and lagged statically pervasive factors. Then, assuming finite lag order, this simplification reduces estimation to a regression of the observed variables on estimated factors and their lags, where the factors are extracted via static principal components. The proposed approach naturally accommodates weak, non-pervasive factors within the dynamic common space. We establish consistency and asymptotic normality for both the dynamic and weak common components under a new asymptotic framework that allows for such weak factors. In an application to three high-dimensional time series panels of European macroeconomic data we detect a sizeable weak common component share in several key macroeconomic indicators.