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Spectral analysis of fractionally cointegrated systems

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  • Nielsen, Morten Orregaard

Abstract

Cointegration imposes restrictions on the frequency domain behavior of a time series at the zero-frequency. We derive these restrictions for a multivariate fractionally cointegrated system. In particular, we consider a p-vector time series integrated of order d with r cointegrating relations, given by the rows of [I_{r};ß'], where the cointegration errors are integrated of order d-b, d=b>0. We show that, at the zero-frequency, the spectral density matrix of the d'th differenced series has reduced rank (p-r), the coherence and phase measures (multiple and partial) equal unity and zero, respectively, and the gain is the matrix of cointegrating coefficients. Extensions to noncontemporaneous cointegration, seasonal cointegration, and different fractional values of b for each cointegrating relation are considered.
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  • Nielsen, Morten Orregaard, 2004. "Spectral analysis of fractionally cointegrated systems," Economics Letters, Elsevier, vol. 83(2), pages 225-231, May.
  • Handle: RePEc:eee:ecolet:v:83:y:2004:i:2:p:225-231
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    References listed on IDEAS

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    1. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    2. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
    3. Daniel Levy, 2002. "Cointegration in Frequency Domain," Emory Economics 0209, Department of Economics, Emory University (Atlanta).
    4. Morten Oerregaard Nielsen, "undated". "Local Whittle Analysis of Stationary Fractional Cointegration," Economics Working Papers 2002-8, Department of Economics and Business Economics, Aarhus University.
    5. Phillips, P. C. B. & Ouliaris, S., 1988. "Testing for cointegration using principal components methods," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 205-230.
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    Cited by:

    1. Kristoufek, Ladislav, 2013. "Mixed-correlated ARFIMA processes for power-law cross-correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6484-6493.
    2. Avarucci, Marco & Velasco, Carlos, 2009. "A Wald test for the cointegration rank in nonstationary fractional systems," Journal of Econometrics, Elsevier, vol. 151(2), pages 178-189, August.
    3. 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.
    4. 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.
    5. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
    6. Nielsen, Morten Orregaard, 2005. "Noncontemporaneous cointegration and the importance of timing," Economics Letters, Elsevier, vol. 86(1), pages 113-119, January.

    More about this item

    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

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