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

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Author Info
Morten Ørregaard Nielsen () (Queen's University and CREATES)
Per Frederiksen () (Nordea Markets)

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Abstract

We consider estimation of the cointegrating relation in the stationary fractional cointegration model. This model has found important application recently, especially in financial economics. Previous research 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 while still having the same asymptotic variance as the NBLS estimator. 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 only has the same asymptotic distribution as if the errors were observed 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 reduce both the 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 proposed methodology.

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File URL: http://www.econ.queensu.ca/working_papers/papers/qed_wp_1171.pdf
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Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1171.

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Length: 41 pages
Date of creation: Jul 2008
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Handle: RePEc:qed:wpaper:1171

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

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C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Federico M. Bandi & Benoit Perron, 2006. "Long Memory and the Relation Between Implied and Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 636-670. [Downloadable!] (restricted)
  2. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Economics Discussion Papers 535, University of Essex, Department of Economics. [Downloadable!]
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  3. 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)
  4. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November. [Downloadable!] (restricted)
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  5. 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. [Downloadable!] (restricted)
  6. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July. [Downloadable!] (restricted)
  7. Christensen, Bent Jesper & Nielsen, Morten Orregaard, 2006. "Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting," Journal of Econometrics, Elsevier, vol. 133(1), pages 343-371, July. [Downloadable!] (restricted)
  8. Juan J. Dolado & Francisco Mármol, 1996. "Efficient Estimation of Cointegrating Relationships Among Higher Order and Fractionally Integrated Processes," Banco de España Working Papers 9617, Banco de España.
  9. Nielsen, Morten Oe., . "Semiparametric Estimation in Time Series Regression with Long Range Dependence," Economics Working Papers 2002-17, School of Economics and Management, University of Aarhus. [Downloadable!]
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  10. Federico Bandi & Benoit Perron, 2003. "Long memory and the relation between implied and realized volatility," Econometrics 0305004, EconWPA. [Downloadable!]
  11. Haldrup, Niels & Nielsen, Morten Orregaard, 2006. "A regime switching long memory model for electricity prices," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 349-376. [Downloadable!] (restricted)
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  12. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February. [Downloadable!] (restricted)
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  13. Lobato, Ignacio N & Robinson, Peter M, 1998. "A Nonparametric Test for I(0)," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 475-95, July. [Downloadable!] (restricted)
  14. Jurgen Doornik & Marius Ooms, 2004. "Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 8(2), pages 1218-1218. [Downloadable!] (restricted)
  15. Lobato, Ignacio N & Velasco, Carlos, 2000. "Long Memory in Stock-Market Trading Volume," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 410-27, October.
  16. Chen, Willa W. & Hurvich, Clifford M., 2003. "Estimating fractional cointegration in the presence of polynomial trends," Journal of Econometrics, Elsevier, vol. 117(1), pages 95-121, November. [Downloadable!] (restricted)
  17. Shimotsu, Katsumi, 2007. "Gaussian semiparametric estimation of multivariate fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 137(2), pages 277-310, April. [Downloadable!] (restricted)
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  18. Chen, Willa W. & Hurvich, Clifford M., 2003. "Semiparametric Estimation of Multivariate Fractional Cointegration," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 629-642, January. [Downloadable!] (restricted)
  19. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
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