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Determination of cointegrating rank in fractional systems

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  • Robinson, Peter
  • Yajima, Yoshihiro

Abstract

This paper develops methods of investigating the existence and extent of cointegration in fractionally integrated systems. We focus on stationary series, with some discussion of extension to nonstationarity. The setting is semiparametric, so that modelling is effectively confined to a neighbourhood of frequency zero. We first discuss the definition of fractional cointegration. The initial step of cointegration analysis entails partitioning the vector series into subsets with identical differencing parameters, by means of a sequence of hypopthesis tests. We then estimate cointegrating rank by analysing each subset individually. Two approaches are considered here, both of which are based on the eigenvalues of an estimate of the normalised spectral density matrix at frequency zero. An empirical application to a trivariate series of oil prices is included.

Suggested Citation

  • Robinson, Peter & Yajima, Yoshihiro, 2001. "Determination of cointegrating rank in fractional systems," LSE Research Online Documents on Economics 2267, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:2267
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    File URL: http://eprints.lse.ac.uk/2267/
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    Cited by:

    1. Nielsen, Morten Ørregaard, 2010. "Nonparametric cointegration analysis of fractional systems with unknown integration orders," Journal of Econometrics, Elsevier, vol. 155(2), pages 170-187, April.
    2. Carlos Pestana Barros & Luis Gil-Alana, 2006. "Eta: A Persistent Phenomenon," Defence and Peace Economics, Taylor & Francis Journals, vol. 17(2), pages 95-116.
    3. Nuno Cassola & Claudio Morana, 2006. "Volatility of interest rates in the euro area: Evidence from high frequency data," The European Journal of Finance, Taylor & Francis Journals, vol. 12(6-7), pages 513-528.
    4. Cunado, J. & Gil-Alana, L.A. & de Gracia, F. Perez, 2005. "A test for rational bubbles in the NASDAQ stock index: A fractionally integrated approach," Journal of Banking & Finance, Elsevier, vol. 29(10), pages 2633-2654, October.

    More about this item

    Keywords

    Fractional cointegration; long memory;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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