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Exact Local Whittle Estimation of Fractionally Cointegrated Systems

  • Shimotsu, Katsumi

Semiparametric estimation of a bivariate fractionally cointegrated system is considered. We propose a two-step procedure that accommodates both (asymptotically) stationary (d =1/2) stochastic trend and/or equilibrium error. A tapered version of the local Whittle estimator of Robinson (2008) is used as the first-stage estimator, and the second-stage estimator employs the exact local Whittle approach of Shimotsu and Phillips (2005). The consistency and asymptotic distribution of the two-step estimator are derived. The estimator of the memory parameters has the same Gaussian asymptotic distribution in both the stationary and nonstationary case. The convergence rate and the asymptotic distribution of the estimator of the cointegrating vector are affected by the difference between the memory parameters. Further, the estimator has a Gaussian asymptotic distribution when the difference between the memory parameters is less than 1/2.

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File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/18681/5/070econDP10-11.pdf
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Paper provided by Graduate School of Economics, Hitotsubashi University in its series Discussion Papers with number 2010-11.

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Length: 34 p.
Date of creation: Sep 2010
Date of revision:
Handle: RePEc:hit:econdp:2010-11
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Web page: http://www.econ.hit-u.ac.jp/

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  2. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
  3. Katsumi Shimotsu, 2003. "Gaussian semiparametric estimation of multivariate fractionally integrated processes," Economics Discussion Papers 571, University of Essex, Department of Economics.
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  17. Tsay, Wen-Jen & Chung, Ching-Fan, 2000. "The spurious regression of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 155-182, May.
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  27. Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Local Whittle Estimation in Nonstationary and Unit Root Cases," Cowles Foundation Discussion Papers 1266, Cowles Foundation for Research in Economics, Yale University, revised Sep 2003.
  28. 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.
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