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Fully Modified Narrow-Band Least Squares Estimation of Stationary Fractional Cointegration

Author

Listed:
  • Morten Ørregaard Nielsen

    () (Queen's University and CREATES)

  • Per Frederiksen

    () (Nordea Markets)

Abstract

We consider estimation of the cointegrating relation in the stationary fractional cointegration model which has found important application recently, especially in financial economics. Previous research on this model has considered a semiparametric narrow-band least squares (NBLS) estimator in the frequency domain, often under a condition of non-coherence between regressors and errors at the zero frequency. We show that in the absence of this condition, the NBLS estimator is asymptotically biased, and also that the bias can be consistently estimated. Consequently, we introduce a fully modified NBLS estimator which eliminates the bias, and indeed enjoys a faster rate of convergence than NBLS in general. We also show that local Whittle estimation of the integration order of the errors can be conducted consistently on the residuals from NBLS regression, whereas the estimator has the same asymptotic distribution as if the errors were observed only under the condition of non-coherence. Furthermore, compared to much previous research, the development of the asymptotic distribution theory is based on a different spectral density representation, which is relevant for multivariate fractionally integrated processes, and the use of this representation is shown to result in lower asymptotic bias and variance of the narrow-band estimators. We also present simulation evidence and a series of empirical illustrations to demonstrate the feasibility and empirical relevance of our methodology.

Suggested Citation

  • Morten Ørregaard Nielsen & Per Frederiksen, 2008. "Fully Modified Narrow-Band Least Squares Estimation of Stationary Fractional Cointegration," Working Papers 1171, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:1171
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    File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1171.pdf
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    References listed on IDEAS

    as
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    Cited by:

    1. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
    2. Esben Hoeg & Per Frederiksen, 2006. "The Fractional OU Process: Term Structure Theory and Application," Computing in Economics and Finance 2006 194, Society for Computational Economics.
    3. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, Department of Economics and Business Economics, Aarhus University.

    More about this item

    Keywords

    Fractional cointegration; frequency domain; fully modified estimation; long memory; semiparametric;

    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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