Cointegration in frequency domain

Daniel Levy ()

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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; Spectrum; Coherence; Phase; Gain; Long Run (search for similar items in EconPapers)
Date: 2002-05
Note: View the original document on HAL open archive server: https://hal.science/hal-02385599
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Citations: View citations in EconPapers (12)

Published in Journal of Time Series Analysis, 2002, 23 (3), pp.333-339. ⟨10.1111/1467-9892.00267⟩

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Related works:
Working Paper: Cointegration in Frequency Domain (2004)
Journal Article: Cointegration in frequency domain (2002)
Journal Article: Cointegration in Frequency Domain (2002)
Working Paper: Cointegration in Frequency Domain (2002)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02385599

DOI: 10.1111/1467-9892.00267

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