| Title: | Cointegration in Frequency Domain* |
| Number: | 02-09 |
| Author: | Daniel Levy |
| Issue Date: | May 2002 |
| 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, Xt and Yt , 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)Xt and (1-L)Yt will equal one, their phase will equal zero, and their gain will equal |b| . |
Journal of Time Series Analysis, 2002.
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