Discovering pervasive and non-pervasive common cycles

The objective of this paper is to propose a strategy to exploit short-run commonalities in the sectoral components of macroeconomic variables to obtain better models and more accurate forecasts of the aggregate and of the components. Our main contribution concerns cases in which the number of components is large, so that traditional multivariate approaches are not feasible. We show analytically and by Monte Carlo methods that subsets of components in which all the elements share a single common cycle can be discovered by pairwise methods. As the procedure does not rely on any kind of cross-sectional averaging strategy: it does not need to assume pervasiveness, it can deal with highly correlated idiosyncratic components and it does not need to assume that the size of the subsets goes to infinity. Nonetheless, the procedure works both with fixed N and T going to infinity, and with T and N both going to infinity.