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Some frequency domain properties of fractionally cointegrated processes


  • Claudio Morana


The paper shows that the multiple squared coherence at the zero frequency for fractionally differenced (fractionally) cointegrated processes is equal to one, while the simple squared coherences assume a value greater than zero but lower than one. In the bivariate case the multiple and simple squared coherence coincide and, therefore, the simple squared coherence at the zero frequency assumes a unitary value. It is also found that processes that are not fractionally cointegrated show, in general, positive, but lower than one, multiple and simple squared coherences at the zero frequency. In the case the dependent and independent variables are driven by different long memory factors, i.e. in the case when the dependent variable is orthogonal at the zero frequency to any of the regressors, the squared multiple coherence will assume a zero value, as any of the squared simple coherences. It is finally shown that all the above results also hold for the series in levels, as the frequency tends to zero.

Suggested Citation

  • Claudio Morana, 2004. "Some frequency domain properties of fractionally cointegrated processes," Applied Economics Letters, Taylor & Francis Journals, vol. 11(14), pages 891-894.
  • Handle: RePEc:taf:apeclt:v:11:y:2004:i:14:p:891-894 DOI: 10.1080/1350485042000261289

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    References listed on IDEAS

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    Cited by:

    1. Nuno Cassola & Claudio Morana, 2008. "Modeling Short-Term Interest Rate Spreads in the Euro Money Market," International Journal of Central Banking, International Journal of Central Banking, vol. 4(4), pages 1-37, December.
    2. Cassola, Nuno & Morana, Claudio, 2010. "Comovements in volatility in the euro money market," Journal of International Money and Finance, Elsevier, vol. 29(3), pages 525-539, April.
    3. Morana, Claudio, 2006. "A small scale macroeconometric model for the Euro-12 area," Economic Modelling, Elsevier, vol. 23(3), pages 391-426, May.
    4. Beltratti, A. & Morana, C., 2006. "Breaks and persistency: macroeconomic causes of stock market volatility," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 151-177.

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