Spectral analysis of fractionally cointegrated systems

Fractional cointegration imposes restrictions on the zero-frequency behavior of a time series. In a multivariate time series, integrated of order d (1/2,3/2) and cointegrating to order d−b (−1/2,1/2), we derive these restrictions in terms of the (reduced) rank of the spectral density matrix of the dth differenced series and in terms of gain, coherence, and phase measures.