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Gaussian estimation of parametric spectral density with unknown pole

Giraitis, L., Hidalgo, J. and Robinson, P.M. (2001) Gaussian estimation of parametric spectral density with unknown pole. Annals of Statistics, 29 (4). pp. 987-1023. ISSN 0090-5364

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We consider a parametric spectral density with power-law behavior about a fractional pole at the unknown frequency $\omega$. The case of known $\omega$, especially $\omega =0$, is standard in the long memory literature. When $omega$ 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 establish $n$-consistency of the estimate of $\omega$, and discuss its (non-standard) limiting distributional behavior. For the remaining parameter estimates,we establish $\sqrt{n}$-consistency and asymptotic normality.

Item Type: Article
Keywords: Long range dependence; unknown pole
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 25 Aug 2009 14:39
Last Modified: 25 Aug 2009 14:39
Published Version: http://dx.doi.org/10.1214/aos/1013699989
Status: Published
Publisher: Institute of Mathematical Statistics
Identification Number: 10.1214/aos/1013699989
URI: http://eprints.whiterose.ac.uk/id/eprint/5617

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