In this article, we propose a cointegration-based Permanent-Transitory decomposition for non-stationary Dynamic Factor Models. Our methodology exploits the cointegration relations among the observable variables and assumes they are driven by a common and an idiosyncratic component. The common component is further split into a long-term non-stationary part and a short-term stationary one. A Monte Carlo experiment shows that taking into account the cointegration structure in the DFM leads to a much better reconstruction of the space spanned by the factors, with respect to the most standard technique of applying a factor model in differenced systems. Finally, an application of our procedure to a set of different commodity prices allows to analyse the comovement among different markets. We find that commodity prices move together due to long-term common forces and that the trend for most primary good prices is declining, whereas metals and energy ones exhibit an upward or at least stable pattern since the 2000s.