The pairwise approach to model a large set of disaggregates with common trends

The objective of this paper is to model and forecast all the components of a macro orbusiness variable. Our contribution concerns cases with a large number (hundreds) ofcomponents where 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 a group of N of them. 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. The asymptotic properties of the procedure are studied analytically. Monte Carlo evidence on the small samples performance is provided and a small samples correction procedure designed. A comparison with a DFM alternative is also carried out, and results indicate that the pairwise approach dominates in many empirically relevant situations. A relevant advantage of the pairwise approach is that it does not need common features to be pervasive. A strategy for dealing with outliers and breaks in the context of the pairwise procedure is designed and its properties studied by Monte Carlo. Results indicate that the treatment of these observations may considerably improve the procedure's performance when series are 'contaminated'.