Cointegration in Frequency Domain

Posted: 13 Feb 2003

See all articles by Daniel Levy

Daniel Levy

Bar-Ilan University - Department of Economics; Emory University - Department of Economics; Rimini Center for Economic Analysis

Multiple version iconThere are 2 versions of this paper


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(t) and Y(t), 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) X(t) and (1 - L) Y(t) will equal one, their phase will equal zero, and their gain will equal |b|.

Keywords: Common Stochastic Trend, Cointegration, Frequency Domain Anlysis, Cross-Spectrum, Zero-Frequency

Keywords: Cointegration, Integration, Frequency Domain Analysis, Zero Frequency, Coherence, Phase, Gain, Bivariate System, Common Stochastic Trend, Spectrum, Cross-Spectrum

JEL Classification: C32, C50, C14

Suggested Citation

Levy, Daniel, Cointegration in Frequency Domain. Journal of Time Series Analysis, Forthcoming, Available at SSRN: or

Daniel Levy (Contact Author)

Bar-Ilan University - Department of Economics ( email )

Ramat-Gan, 5290002
+972 3 531-8345 (Phone)
+972 3 738-4034 (Fax)


Emory University - Department of Economics ( email )

1602 Fishburne Drive, Suite 306
Rich Building
Atlanta, GA 30322-0001
United States


Rimini Center for Economic Analysis ( email )

Wilfrid Laurier University
75 University Ave W.
Waterloo, Ontario N2L3C5


Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
PlumX Metrics