This paper explores the possibility of cointegration existing between processes integrated at di¤erent frequencies. Using the demodulator operator, we show that such cointegration can exist and explore its form using both complex- and real-valued representations. A straightforward approach to...

This paper explores the possibility of cointegration existing between processes integrated at di¤erent frequencies. Using the demodulator operator, we show that such cointegration can exist and explore its form using both complex- and real-valued representations. A straightforward approach to...

To understand the impact of temporal aggregation on the properties of a seasonal long-memory process, the effects of skip and cumulation sampling on both stationary and nonstationary processes with poles at several potential frequencies are analyzed. By allowing for several poles in the...

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,...

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,...

Seasonality is pervasive across a wide range of economic time series and it substantially complicates the analysis of unit root non-stationarity in such series. This paper reviews recent contributions to the literature on non-stationary seasonal processes, focussing on periodically integrated (P...

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...