Abstract
Existence of a cointegration relationship between two time series in the time domain imposes restrictions on the series zero-frequency behaviour in terms of their squared coherence, phase and gain, in the frequency domain. I derive these restrictions by studying cross-spectral properties of a cointegrated bivariate system. Specifically, I demonstrate that if two difference stationary series, X and Y, are cointegrated with a cointegrating vector (1 b) and thus share a common stochastic trend, then at the zero frequency, the squared coherence of (1 - L) and (1 - L) will equal one, their phase will equal zero, and their gain will equal (b).
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