CEBA Talk: Testing for the cointegration rank between Periodically Integrated processes

Abstract: Cointegration between Periodically Integrated (PI) processes has been analyzed among other by Birchen- hall, 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). However, so far there is not a method, published in an academic journal, that allows us to determine the cointegration rank between PI processes. This paper fills the gap, a method to determine the cointegration rank between a set PI Processes based on the idea of pseudo-demodulation is proposed in the context of Seasonal Cointegration by del Barrio Castro, Cubadda and Osborn (2020). Once a pseudo-demodulation time series is obtained the Johansen (1995) procedure could be applied to determine the cointegration rank. A Monte Carlo experiment shows that the proposed approach works satisfactorily for small samples.