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August 2001 Gaussian estimation of parametric spectral density with unknown pole
L. Giraitis, J. Hidalgo, P. M. Robinson
Ann. Statist. 29(4): 987-1023 (August 2001). DOI: 10.1214/aos/1013699989


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.


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L. Giraitis. J. Hidalgo. P. M. Robinson. "Gaussian estimation of parametric spectral density with unknown pole." Ann. Statist. 29 (4) 987 - 1023, August 2001.


Published: August 2001
First available in Project Euclid: 14 February 2002

zbMATH: 1012.62098
MathSciNet: MR1869236
Digital Object Identifier: 10.1214/aos/1013699989

Primary: 62M10
Secondary: 60G18

Keywords: Long range dependence , unknown pole

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 4 • August 2001
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