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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Abstract

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 Long range dependence; unknown pole The University of York The University of York > Mathematics (York) York RAE Import 25 Aug 2009 14:39 25 Aug 2009 14:39 http://dx.doi.org/10.1214/aos/1013699989 Published Institute of Mathematical Statistics 10.1214/aos/1013699989 http://eprints.whiterose.ac.uk/id/eprint/5617