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Cointegration in Fractional Systems with Unkown Integration Orders

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Javier Hualde
Peter M Robinson

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Abstract

The semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is completely known. However in moderate samples the normal approximation may not be very good, so we consider a refined, Edgeworth, approximation, for both a tapered estimate, and the original untapered one. For the tapered estimate, our higher-order correction involves two terms, one of order 1/vm (where m is the bandwidth number in the estimation), the other a bias term, which increases in m; depending on the relative magnitude of the terms, one or the other may dominate, or they may balance. For the untapered estimate we obtain an expansion in which, for m increasing fast enough, the correction consists only of a bias term. We discuss applications of our expansions to improved statistical inference and bandwidth choice. We assume Gaussianity, but in other respects our assumptions seem mild.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2003/449.

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Date of creation: Feb 2003
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Handle: RePEc:cep:stiecm:/2003/449

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Keywords: Fractional cointegration; unknown integration orders; system estimates; mixed normal asymptotics.;

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  1. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September. [Downloadable!] (restricted)
  2. P.M. Robinson & D. Marinucci, 2000. "The Averaged Periodogram for Nonstationary Vector Time Series," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 149-160, January. [Downloadable!] (restricted)
  3. D Marinucci & Peter M Robinson, 2000. "The Averaged Periodogram for Nonstationary Vector Time Series," STICERD - Econometrics Paper Series /2000/408, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  1. Javier Hualde & Peter M. Robinson, 2002. "Root-n-Consistent Estimation of Weak Fractional Cointegration," Faculty Working Papers 08/02, School of Economics and Business Administration, University of Navarra. [Downloadable!]
  2. J. Cunado & L.A. Gil-Alana & F. Perez De Gracia, 2007. "Real convergence in some emerging countries : a fractionally integrated approach," Discussion Papers (REL - Recherches Economiques de Louvain) 2007034, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
    Other versions:
  3. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2005. "Fractional Cointegration And Aggregate Money Demand Functions," Economics and Finance Discussion Papers 05-01, Economics and Finance Section, School of Social Sciences, Brunel University. [Downloadable!]
    Other versions:
  4. Marco Avarucci & Domenico Marinucci, 2005. "Polynomial Cointegration Among Stationary Processes With Long Memory," Economics Working Papers we055123, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  5. Hurvich, Cliiford & Wang, Yi, 2006. "A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects," MPRA Paper 1413, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  6. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, School of Economics and Management, University of Aarhus. [Downloadable!]
  7. Morten Ørregaard Nielsen, 2009. "Nonparametric Cointegration Analysis of Fractional Systems With Unknown Integration Orders," CREATES Research Papers 2009-02, School of Economics and Management, University of Aarhus. [Downloadable!]
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  8. Katarzyna Lasak, 2008. "Likelihood based testing for no fractional cointegration," CREATES Research Papers 2008-52, School of Economics and Management, University of Aarhus. [Downloadable!]
  9. M. Gerolimetto & Peter M Robinson, 2006. "Instrumental Variables Estimation of Stationaryand Nonstationary Cointegrating Regressions," STICERD - Econometrics Paper Series /2006/500, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  10. Fabrizio Iacone & Peter M Robinson, 2004. "Cointegration in Fractional Systems with Deterministic Trends," STICERD - Econometrics Paper Series /2004/476, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  11. Carlos Pestana Barros & João Ricardo Faria & Luis A. Gil-Alana, 2008. "Persistence in Airline Accidents," Working Papers 2008/18, Department of Economics at the School of Economics and Management (ISEG), Technical University of Lisbon.. [Downloadable!]
  12. Luis A. Gil-Alana, 2004. "Fractional cointegration in the consumption and income relationship using semiparametric techniques," Economics Bulletin, Economics Bulletin, vol. 3(47), pages 1-8. [Downloadable!]
  13. Javier Hualde & Peter M Robinson, 2006. "Root-N-Consistent Estimation Of Weakfractional Cointegration," STICERD - Econometrics Paper Series /2006/499, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  14. Ignacio N. Lobato & Carlos Velasco, 2005. "Efficient Wald Tests For Fractional Unit Roots," Economics Working Papers we056935, Universidad Carlos III, Departamento de Economía. [Downloadable!]
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  15. Javier Hualde, 2005. "Unbalanced Cointegration," Faculty Working Papers 06/05, School of Economics and Business Administration, University of Navarra. [Downloadable!]
  16. Javier Hualde & Peter M Robinson, 2006. "Semiparametric Estimation of Fractional Cointegration," STICERD - Econometrics Paper Series /2006/502, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  17. Peter M Robinson, 2004. "The Distance between Rival Nonstationary Fractional Processes," STICERD - Econometrics Paper Series /2004/468, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  18. Luis A. Gil-Alana, 2003. "Testing of Fractional Cointegration in Macroeconomic Time Series," Faculty Working Papers 09/03, School of Economics and Business Administration, University of Navarra. [Downloadable!]
    Other versions:
  19. Katsumi Shimotsu & Morten Ørregaard Nielsen, 2006. "Determining the Cointegrating Rank in Nonstationary Fractional Systems by the Exact Local Whittle Approach," Working Papers 1029, Queen's University, Department of Economics. [Downloadable!]
    Other versions:
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