Cointegration in frequency domain

D. Levy

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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|.

Original languageEnglish
Pages (from-to)333-339
Number of pages7
JournalJournal of Time Series Analysis
Issue number3
StatePublished - May 2002
Externally publishedYes


  • Cointegration
  • Common stochastic trend
  • Cross-spectrum
  • Frequency domain analysis
  • Zero-frequency


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