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Semiparametric Estimation of Fractional Cointegration

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Author Info
Javier Hualde
Peter M Robinson
Abstract

A semiparametric bivariate fractionally cointegrated system is considered, integrationorders possibly being unknown and I (0) unobservable inputs having nonparametricspectral density. Two kinds of estimate of the cointegrating parameter ? are considered,one involving inverse spectral weighting and the other, unweighted statistics with a spectralestimate at frequency zero. We establish under quite general conditions the asymptoticdistributional properties of the estimates of ?, both in case of "strong cointegration" (whenthe difference between integration orders of observables and cointegrating errors exceeds1/2) and in case of "weak cointegration" (when that difference is less than 1/2), whichincludes the case of (asymptotically) stationary observables. Across both cases, the sameWald test statistic has the same standard null ?2 limit distribution, irrespective of whetherintegration orders are known or estimated. The regularity conditions include unprimitiveones on the integration orders and spectral density estimates, but we check these undermore primitive conditions on particular estimates. Finite-sample properties are examined ina Monte Carlo study.

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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 /2006/502.

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Date of creation: May 2006
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Handle: RePEc:cep:stiecm:/2006/502

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Related research
Keywords: Fractional cointegration; semiparametric model; unknown integration orders.;

Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

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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.:
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    Other versions:
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    Other versions:
  6. P. M. Robinson & J. Hualde, 2003. "Cointegration in Fractional Systems with Unknown Integration Orders," Econometrica, Econometric Society, vol. 71(6), pages 1727-1766, November. [Downloadable!] (restricted)
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  7. Donald W. K. Andrews & Yixiao Sun, 2004. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Econometrica, Econometric Society, vol. 72(2), pages 569-614, 03. [Downloadable!] (restricted)
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  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. [Downloadable!]
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(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. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, School of Economics and Management, University of Aarhus. [Downloadable!]
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