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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. Katsumi Shimotsu, 2006. "Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend," Working Papers 1061, Queen's University, Department of Economics.
  3. Hassler, Uwe & Marmol, Francesc & Velasco, Carlos, 2002. "Residual Log-Periodogram Inference for Long-Run-Relationships," Darmstadt Discussion Papers in Economics 37317, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute of Economics (VWL).
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