On cointegration for processes integrated at different frequencies

This article explores the possibility of cointegration existing between processes integrated at different 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 test for the presence of cointegration between processes integrated at different frequencies is proposed, with a Monte Carlo study and an application showing that the testing approach works well.