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Spectral Analysis of Fractionally Cointegrated Systems

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  • Nielsen, Morten Oe.

    ()
    (Department of Economics, University of Aarhus, Denmark)

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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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 2002-12.

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Length: 10
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Handle: RePEc:aah:aarhec:2002-12

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Common stochastic trend; fractional cointegration; frequency domain analysis; reduced rank; zero-frequency.;

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  1. 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.
  2. Morten Oerregaard Nielsen, . "Local Whittle Analysis of Stationary Fractional Cointegration," Economics Working Papers 2002-8, School of Economics and Management, University of Aarhus.
  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, 2004. "Cointegration in Frequency Domain," Econometrics 0402005, EconWPA.
  5. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
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Cited by:
  1. 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.
  2. Nielsen, Morten Orregaard, 2005. "Noncontemporaneous cointegration and the importance of timing," Economics Letters, Elsevier, vol. 86(1), pages 113-119, January.
  3. Ladislav Kristoufek, 2013. "Mixed-correlated ARFIMA processes for power-law cross-correlations," Papers 1307.6046, arXiv.org, revised Aug 2013.
  4. 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.

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