Combining economic time series with the aim to obtain an indicator for business cycle analyses is an important issue for policy makers. In this area, econometric techniques usually rely on systems with either a small number of series, N, (VAR or VECM) or, at the other extreme, a very large N (factor models). In this paper we propose tools to select the relevant business cycle indicators in a "medium" N framework, a situation that is likely to be the most frequent in empirical works. An example is provided by our empirical application, in which we study jointly the short-run co-movements of 24 European countries. We show, under not too restrictive conditions, that parsimonious single-equation models can be used to split a set of N countries in three groups. The first group comprises countries that share a synchronous common cycle, a non-synchronous common cycle is present among the countries of the second group, and the third group collects countries that exhibit idiosyncratic cycles. Moreover, we offer a method for constructing a composite coincident indicator that explicitly takes into account the existence of these various forms of short-run co-movements among variables.