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

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  • Morten Ørregaard Nielsen

    () (Queen's University and CREATES)

  • Per Frederiksen

    () (Nordea Markets)

Abstract

We consider estimation of the cointegrating relation in the weak fractional cointegration model, where the strength of the cointegrating relation (difference in memory parameters) is less than one-half. A special case is 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, but in the stationary case its asymptotic distribution has been derived only 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 based on NBLS residuals, but 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 present simulation evidence and a series of empirical illustrations to demonstrate the feasibility and empirical relevance of our methodology.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1226.pdf
File Function: First version 2010
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1226.

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Length: 35 pages
Date of creation: May 2010
Date of revision:
Handle: RePEc:qed:wpaper:1226

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

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Cited by:
  1. Marcel Aloy & Gilles de Truchis, 2012. "Estimation and Testing for Fractional Cointegration," AMSE Working Papers 1215, Aix-Marseille School of Economics, Marseille, France.
  2. Luis A. Gil-Alana & Guglielmo Maria Caporale, 2012. "Fractional Integration and Cointegration in US Financial Time Series Data," Faculty Working Papers 12/12, School of Economics and Business Administration, University of Navarra.
  3. Gilles De Truchis, 2012. "Approximate Whittle Analysis of Fractional Cointegration and the Stock Market Synchronization Issue," Working Papers halshs-00793220, HAL.
  4. Jozef Barunik & Michaela Barunikova, 2012. "Revisiting the fractional cointegrating dynamics of implied-realized volatility relation with wavelet band spectrum regression," Papers 1208.4831, arXiv.org, revised Feb 2013.

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