Spectral Analysis of Fractionally Cointegrated Systems

Morten Nielsen

Economics Working Papers from Department of Economics and Business Economics, Aarhus University

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.

Keywords: Common stochastic trend; fractional cointegration; frequency domain analysis; reduced rank; zero-frequency. (search for similar items in EconPapers)
JEL-codes: C32 (search for similar items in EconPapers)
Pages: 10
New Economics Papers: this item is included in nep-ecm and nep-rmg
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Spectral analysis of fractionally cointegrated systems (2004)
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Persistent link: https://EconPapers.repec.org/RePEc:aah:aarhec:2002-12

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