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Semiparametric Estimation of Fractional Cointegration

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  • Javier Hualde

    ()
    (Universidad de Navarra)

  • Peter Robinson

    ()
    (London School of Economics)

Abstract

A semiparametric bivariate fractionally cointegrated system is considered, integration orders possibly being unknown and I(0) unobservable inputs having nonparametric spectral density. Two kinds of estimate of the cointegrating parameter ν are considered, one involving inverse spectral weighting and the other, unweighted statistics with a spectral estimate at frequency zero. We establish under quite general conditions the asymptotic distributional properties of the estimates of ν, both in case of "strong cointegration" (when the difference between integration orders of observables and cointegrating errors exceeds 1/2) and in case of "weak cointegration" (when that difference is less than 1/2), which includes the case of (asymptotically) stationary observables. Across both cases, the same Wald test statistic has the same standard null χ² limit distribution, irrespective of whether integration orders are known or estimated. The regularity conditions include unprimitive ones on the integration orders and spectral density estimates, but we check these under more primitive conditions on particular estimates. Finite-sample properties are examined in a Monte Carlo study.A semiparametric bivariate fractionally cointegrated system is considered, integration orders possibly being unknown and I(0) unobservable inputs having nonparametric spectral density. Two kinds of estimate of the cointegrating parameter ν are considered, one involving inverse spectral weighting and the other, unweighted statistics with a spectral estimate at frequency zero. We establish under quite general conditions the asymptotic distributional properties of the estimates of ν, both in case of "strong cointegration" (when the difference between integration orders of observables and cointegrating errors exceeds 1/2) and in case of "weak cointegration" (when that difference is less than 1/2), which includes the case of (asymptotically) stationary observables. Across both cases, the same Wald test statistic has the same standard null χ² limit distribution, irrespective of whether integration orders are known or estimated. The regularity conditions include unprimitive ones on the integration orders and spectral density estimates, but we check these under more primitive conditions on particular estimates. Finite-sample properties are examined in a Monte Carlo study.

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Bibliographic Info

Paper provided by School of Economics and Business Administration, University of Navarra in its series Faculty Working Papers with number 07/06.

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Length: 48 pages
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Handle: RePEc:una:unccee:wp0706

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Web page: http://www.unav.es/facultad/econom

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References

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  1. ANDREWS, DONALD W & Sun, Yixiao X, 2002. "Adaptive Local Polynomial Whittle Estimation of Long-Range Dependence," University of California at San Diego, Economics Working Paper Series qt9wt048tt, Department of Economics, UC San Diego.
  2. repec:fth:baesse:9617 is not listed on IDEAS
  3. Peter M. Robinson & Javier Hualde, 2002. "Cointegration in Fractional Systems with Unknown Integration Orders," Faculty Working Papers 07/02, School of Economics and Business Administration, University of Navarra.
  4. D Marinucci & Peter M Robinson, 2001. "Narrow-Band Analysis of Nonstationary Processes," STICERD - Econometrics Paper Series /2001/421, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  5. Robinson, Peter M. & Henry, Marc, 2003. "Higher-order kernel semiparametric M-estimation of long memory," Journal of Econometrics, Elsevier, vol. 114(1), pages 1-27, May.
  6. D. Marinucci & Peter M. Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics 303, London School of Economics and Political Science, LSE Library.
  7. Wooldridge, Jeffrey M., 1986. "Estimation and inference for dependent processes," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 45, pages 2639-2738 Elsevier.
  8. Bent Jesper Christensen & Morten Ø. Nielsen, . "Semiparametric Analysis of Stationary Fractional Cointegration and the Implied-Realized Volatility Relation in High-Frequency Options Data," Economics Working Papers 2001-4, School of Economics and Management, University of Aarhus.
  9. D Marinucci & Peter Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics 2015, London School of Economics and Political Science, LSE Library.
  10. 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.
  11. 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.
  12. Juan J. Dolado & Francisco Mármol, 1996. "Efficient Estimation of Cointegrating Relationships Among Higher Order and Fractionally Integrated Processes," Banco de Espa�a Working Papers 9617, Banco de Espa�a.
  13. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
  14. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(04), pages 583-621, August.
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Citations

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Cited by:
  1. Afonso Gonçalves da Silva & Peter M Robinson, 2007. "Fractional Cointegration In StochasticVolatility Models," STICERD - Econometrics Paper Series /2007/519, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. Afonso Goncalves da Silva & Peter Robinson, 2008. "Finite Sample Performance in Cointegration Analysis of Nonlinear Time Series with Long Memory," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 268-297.
  3. P. M. Robinson & M. Gerolimetto, 2006. "Instrumental variables estimation of stationary and non-stationary cointegrating regressions," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 291-306, 07.
  4. Javier Hualde, 2012. "Estimation of the cointegrating rank in fractional cointegration," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 1205, Departamento de Economía - Universidad Pública de Navarra.
  5. 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.
  6. Avarucci, Marco & Velasco, Carlos, 2008. "A Wald Test for the Cointegration Rank in Nonstationary Fractional Systems," Research Memorandum 049, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  7. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, School of Economics and Management, University of Aarhus.
  8. Peter M. Robinson & M. Gerolimetto, 2006. "Instrumental variables estimation of stationary and nonstationary cointegrating regressions," LSE Research Online Documents on Economics 4539, London School of Economics and Political Science, LSE Library.
  9. Peter M Robinson, 2007. "Multiple Local Whittle Estimation in StationarySystems," STICERD - Econometrics Paper Series /2007/525, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  10. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
  11. Peter M. Robinson, 2007. "Multiple local whittle estimation in stationary systems," LSE Research Online Documents on Economics 4436, London School of Economics and Political Science, LSE Library.
  12. Javier Hualde, 2005. "Unbalanced Cointegration," Faculty Working Papers 06/05, School of Economics and Business Administration, University of Navarra.

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