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Non parametric Fractional Cointegration Analysis

  • Mauro Costantini

    (ISAE - Institute for Studies and Economic Analyses)

  • Roy Cerqueti

    (Università degli Studi di Roma “La Sapienza”, Italy)

This paper provides a theoretical fractional cointegration analysis in a nonparametric framework. We solve a generalized eigenvalues problem. To this end, a couple of random matrices are constructed taking into account the stationarity properties of the differencesof a fractional p-variate integrated process. These difference orders are assumed to vary in a continuous and discrete range. The random matrices are defined by some weight functions. Asymptotic behaviors of these random matrices are obtained by stating some conditions on the weight functions, and by using Bierens (1997) and Andersen et al.(1983) results. In this way, a nonparametric analysis is provided. Moving from the solution of the generalized eigenvalue problem, a fractional nonparametric VAR model for cointegration is also presented.

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Paper provided by ISTAT - Italian National Institute of Statistics - (Rome, ITALY) in its series ISAE Working Papers with number 78.

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Length: 31 pages
Date of creation: Feb 2007
Date of revision:
Handle: RePEc:isa:wpaper:78
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  1. Davidson, James, 2002. "A model of fractional cointegration, and tests for cointegration using the bootstrap," Journal of Econometrics, Elsevier, vol. 110(2), pages 187-212, October.
  2. Marmol, Francesc & Escribano, Alvaro & Aparicio, Felipe M., 2002. "Instrumental Variable Interpretation Of Cointegration With Inference Results For Fractional Cointegration," Econometric Theory, Cambridge University Press, vol. 18(03), pages 646-672, June.
  3. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
  4. Bierens, Herman J., 1997. "Nonparametric cointegration analysis," Journal of Econometrics, Elsevier, vol. 77(2), pages 379-404, April.
  5. Nielsen M.O., 2004. "Optimal Residual-Based Tests for Fractional Cointegration and Exchange Rate Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 331-345, July.
  6. Joerg Breitung and Uwe Hassler, 2001. "Inference on the Cointegration Rank in Fractionally Integrated Processes," Computing in Economics and Finance 2001 233, Society for Computational Economics.
  7. 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.
  8. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(04), pages 583-621, August.
  9. Francesc Marmol & Carlos Velasco, 2004. "Consistent Testing of Cointegrating Relationships," Econometrica, Econometric Society, vol. 72(6), pages 1809-1844, November.
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