Cointegration in Frequency Domain

Daniel Levy ()

Econometrics from University Library of Munich, Germany

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; Integration; Frequency Domain Anlysis; Cross-Spectrum; Zero-Frequency; Coherence; Squared Coherence; Phase; Gain; Cross-Spectral Properties; Bivariate Cointegrated System; Long Run Comovement (search for similar items in EconPapers)
JEL-codes: C14 C32 C50 E30 O40 (search for similar items in EconPapers)
Pages: 14 pages
Date: 2004-02-07
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-rmg
Note: Type of Document - pdf; prepared on Win 98; to print on Any printer; pages: 14 ; figures: There are no figures
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Cointegration in frequency domain (2002)
Journal Article: Cointegration in Frequency Domain (2002)
Working Paper: Cointegration in Frequency Domain (2002)
Working Paper: Cointegration in frequency domain (2002)
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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpem:0402005

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