Cointegration in Frequency Domain
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 Yt- 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|.
|Date of creation:||May 2002|
|Date of revision:|
|Contact details of provider:|| Postal: Faculty of Social Sciences, Bar Ilan University 52900 Ramat-Gan|
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- Engle, Robert & Granger, Clive, 2015.
"Co-integration and error correction: Representation, estimation, and testing,"
Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- Daniel Levy, 2005.
"Investment-Saving Comovement and Capital Mobility: Evidence from Century Long U.S. Time Series,"
0505006, EconWPA, revised 16 May 2005.
- Daniel Levy, 2000. "Investment-Saving Comovement and Capital Mobility: Evidence from Century Long U.S. Time Series," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(1), pages 100-137, January.
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