Discovering common trends in a large set of disaggregates: statistical procedures and their properties

The objective of this paper is to model all the N components of a macro or business variable. Our contribution concerns cases with a large number (hundreds) of components, for which multivariate approaches are not feasible. We extend in several directions the pairwise approach originally proposed by Espasa and Mayo-Burgos (2013) and study its statistical properties. The pairwise approach consists on performing common features tests between the N(N-1)/2 pairs of series that exist in the aggregate. Once this is done, groups of series that share common features can be formed. Next, all the components are forecast using single equation models that include the restrictions derived by the common features. In this paper we focus on discovering groups of components that share single common trends. We study analytically the asymptotic properties of the procedure. We also carry out a comparison with a DFM alternative; results indicate that the pairwise approach dominates in many empirically relevant situations. A clear advantage of the pairwise approach is that it does not need common features to be pervasive.