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.

Suggested citation: C. Casoli, R. Lucchetti, (2021), ‘Permanent-Transitory decomposition of cointegrated time series via Dynamic Factor Models, with an application to commodity prices’, Nota di Lavoro 19.2021, Milano, Italy: Fondazione Eni Enrico Mattei