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Gaussian Estimation of Parametric Spectral Density with Unknown Pole

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  • Liudas Giraitis
  • Javier Hidalgo
  • Peter M Robinson

Abstract

We consider a parametric spectral density with power-law behaviour about a fractional pole at the unknown frequency w. The case of unknown w, especially w = 0, is standard in the long memory literature. When w is unknown, asymptotic distribution theory for estimates of parameters, including the (long) memory parameter, is significantly harder. We study a form of Gaussian estimate. We establsih n-consistency of the estimate of w, and discuss its (non-standard) limiting distributional behaviour. For the remaining parameter estimates, we establish Vn-consistency and asymptotic normality.

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File URL: http://sticerd.lse.ac.uk/dps/em/em424.pdf
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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2001/424.

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Date of creation: Aug 2001
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Handle: RePEc:cep:stiecm:/2001/424

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

Keywords: Long-range dependence; unknown pole.;

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  1. Robinson, P. M., 1978. "Alternative models for stationary stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 8(2), pages 141-152, December.
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