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Determination of Cointegrating Rank in Fractional Systems

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Author Info
Peter M Robinson
Yoshihiro Yajima

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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.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2001/423.

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Date of creation: Jul 2001
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Handle: RePEc:cep:stiecm:/2001/423

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Keywords: Fractional cointegration; long memory.;

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References listed on IDEAS
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  1. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June. [Downloadable!] (restricted)
  2. Lobato, Ignacio N., 1999. "A semiparametric two-step estimator in a multivariate long memory model," Journal of Econometrics, Elsevier, vol. 90(1), pages 129-153, May. [Downloadable!] (restricted)
  3. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March. [Downloadable!] (restricted)
  4. James MacKinnon, 1990. "Critical Values for Cointegration Tests," University of California at San Diego, Economics Working Paper Series 90-4, Department of Economics, UC San Diego. [Downloadable!]
  5. Flores, Renato Jr. & Szafarz, Ariane, 1996. "An enlarged definition of cointegration," Economics Letters, Elsevier, vol. 50(2), pages 193-195, February. [Downloadable!] (restricted)
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  6. Diebold, Francis X. & Rudebusch, Glenn D., 1991. "On the power of Dickey-Fuller tests against fractional alternatives," Economics Letters, Elsevier, vol. 35(2), pages 155-160, February. [Downloadable!] (restricted)
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  7. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-12, January.
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