This paper 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...

This paper examines the distributions of (zero frequency) unit root test statistics for I(1) processes in the presence of noninvertible moving average components. The analysis initially considers a noninvertible MA(1), for which the asymptotic distribution of the ADF test statistic under the...