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Semiparametric Estimation of Fractional Cointegration

  • Javier Hualde

    ()

    (Universidad de Navarra)

  • Peter Robinson

    ()

    (London School of Economics)

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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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
Date of creation:
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Handle: RePEc:una:unccee:wp0706
Contact details of provider: Web page: http://www.unav.es/facultad/econom

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  1. Donald W.K. Andrews & Yixiao Sun, 2002. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Cowles Foundation Discussion Papers 1384, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. 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.
  4. 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.
  5. Javier Hualde & Peter M Robinson, 2003. "Cointegration in Fractional Systems with Unkown Integration Orders," STICERD - Econometrics Paper Series /2003/449, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  6. 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.
  7. Marc Henry & Peter M Robinson, 2002. "Higher-Order Kernel Semiparametric M-Estimation of Long Memory," STICERD - Econometrics Paper Series /2002/436, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  8. 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.
  9. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
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