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

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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(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: https://ssrn.com/abstract=372843 or http://dx.doi.org/10.2139/ssrn.372843

Daniel Levy (Contact Author)

Bar-Ilan University - Department of Economics ( email )

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HOME PAGE: http://econ.biu.ac.il/en/levy

Emory University - Department of Economics ( email )

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Rimini Center for Economic Analysis ( email )

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Canada

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