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Spectral analysis of fractionally cointegrated systems

  • Nielsen, Morten Orregaard

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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Article provided by Elsevier in its journal Economics Letters.

Volume (Year): 83 (2004)
Issue (Month): 2 (May)
Pages: 225-231

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Handle: RePEc:eee:ecolet:v:83:y:2004:i:2:p:225-231
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  1. Peter M Robinson & Yoshihiro Yajima, 2001. "Determination of Cointegrating Rank in Fractional Systems," STICERD - Econometrics Paper Series /2001/423, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  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. 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.
  4. Daniel Levy, 2002. "Cointegration in Frequency Domain," Emory Economics 0209, Department of Economics, Emory University (Atlanta).
  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.
  6. Morten Oerregaard Nielsen, . "Local Whittle Analysis of Stationary Fractional Cointegration," Economics Working Papers 2002-8, School of Economics and Management, University of Aarhus.
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