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Cointegration in Frequency Domain

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  • Daniel Levy

    (Department of Economics, Bar Ilan University)

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 and Yt- 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|.

Suggested Citation

  • Daniel Levy, 2002. "Cointegration in Frequency Domain," Working Papers 2002-12, Bar-Ilan University, Department of Economics.
    • Handle: RePEc:biu:wpaper:2002-12
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    References listed on IDEAS

    as
    1. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    2. Daniel Levy, 2000. "Investment-Saving Comovement and Capital Mobility: Evidence from Century Long U.S. Time Series," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(1), pages 100-137, January.
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    Cited by:

    1. Nielsen, Morten Orregaard, 2004. "Spectral analysis of fractionally cointegrated systems," Economics Letters, Elsevier, vol. 83(2), pages 225-231, May.
    2. Claudio Morana, 2004. "Some frequency domain properties of fractionally cointegrated processes," Applied Economics Letters, Taylor & Francis Journals, vol. 11(14), pages 891-894.
    3. Javier Fernandez-Macho, 2013. "A wavelet approach to multiple cointegration testing," Economics Series Working Papers 668, University of Oxford, Department of Economics.
    4. Ramos Francia Manuel & Noriega Antonio E. & Rodríguez-Pérez Cid Alonso, 2015. "The Use of Monetary Aggregates as Indicators of the Future Evolution of Consumer Prices: Monetary Growth and Inflation Target," Working Papers 2015-14, Banco de México.
    5. E. E. Ioannidis & G. A. Chronis, 2005. "Extreme Spectra of Var Models and Orders of Near‐Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 399-421, May.
    6. Eroğlu, Burak Alparslan, 2019. "Wavelet variance ratio cointegration test and wavestrapping," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 298-319.
    7. Claudio Morana, 2004. "Frequency domain principal components estimation of fractionally cointegrated processes," Applied Economics Letters, Taylor & Francis Journals, vol. 11(13), pages 837-842.
    8. Chiquiar Daniel & Ramos Francia Manuel, 2004. "Bilateral Trade and Business Cycle Synchronization: Evidence from Mexico and United States Manufacturing Industries," Working Papers 2004-05, Banco de México.
    9. Patrick J. Wilson & L.J. Perry, 2004. "Forecasting Australian Unemployment Rates using Spectral Analysis," Australian Journal of Labour Economics (AJLE), Bankwest Curtin Economics Centre (BCEC), Curtin Business School, vol. 7(4), pages 459-480, December.
    10. Burak Eroglu, 2017. "Wavelet Variance Ratio Test And Wavestrapping For The Determination Of The Cointegration Rank," Working Papers 1706, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.
    11. Torre Cepeda Leonardo E. & Flores Segovia Miguel A., 2020. "Private Banking Credit and Economic Growth in Mexico: A State Level Panel Data Analysis 2005-2018," Working Papers 2020-17, Banco de México.
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    13. Burak Eroglu & Kemal Caglar Gogebakan & Mirza Trokic, 2017. "Fractional Seasonal Variance Ratio Unit Root Tests," Working Papers 1707, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.
    14. Garcés Díaz Daniel, 2020. "On the Drivers of Inflation in Different Monetary Regimes," Working Papers 2020-16, Banco de México.

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    More about this item

    Keywords

    Common Stochastic Trend; Cointegration; Frequency Domain Anlysis; Cross-Spectrum; Zero-Frequency.;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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