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Non parametric Fractional Cointegration Analysis

Author

Listed:
  • Mauro Costantini

    (ISAE - Institute for Studies and Economic Analyses)

  • Roy Cerqueti

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

Abstract

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.

Suggested Citation

  • Mauro Costantini & Roy Cerqueti, 2007. "Non parametric Fractional Cointegration Analysis," ISAE Working Papers 78, ISTAT - Italian National Institute of Statistics - (Rome, ITALY).
    • Handle: RePEc:isa:wpaper:78
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    References listed on IDEAS

    as
    1. 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.
    2. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
    3. Breitung, Jorg & Hassler, Uwe, 2002. "Inference on the cointegration rank in fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 110(2), pages 167-185, October.
    4. 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.
    5. 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(3), pages 646-672, June.
    6. Bierens, Herman J., 1997. "Nonparametric cointegration analysis," Journal of Econometrics, Elsevier, vol. 77(2), pages 379-404, April.
    7. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(4), pages 583-621, August.
    8. 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.
    9. Francesc Marmol & Carlos Velasco, 2004. "Consistent Testing of Cointegrating Relationships," Econometrica, Econometric Society, vol. 72(6), pages 1809-1844, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Fractional integrated process; Nonparametric methods; Cointegration; Asymptotic distribution; Generalized eigenvalues problem.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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