Testing for the cointegration rank between Periodically Integrated processes

Cointegration between periodically integrated (PI) processes has been analyzed by many, including Bladen-Hovell, Chui, Osborn, and Smith (1989), Boswijk and Franses (1995), Franses and Paap (2004), Kleibergen and Franses (1999) and del Barrio Castro and Osborn (2008), to name a few. However, there is currently no published method that allows us to determine the cointegration rank between P I processes. The present paper Ölls this gap in the literature with a method for determining the cointegration rank between a set of P I processes based on the idea of pseudo-demodulation, as proposed in the context of seasonal cointegration by del Barrio Castro, Cubadda, and Osborn (2020). Once a pseudodemodulated time series is obtained, the Johansen (1995) procedure can be applied to determine the cointegration rank. A Monte Carlo experiment shows that the proposed approach works satisfactorily for small samples.