The Annals of Statistics

Gaussian estimation of parametric spectral density with unknown pole

L. Giraitis, J. Hidalgo, and P. M. Robinson

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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.

Article information

Source
Ann. Statist., Volume 29, Number 4 (2001), 987-1023.

Dates
First available in Project Euclid: 14 February 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1013699989

Digital Object Identifier
doi:10.1214/aos/1013699989

Mathematical Reviews number (MathSciNet)
MR1869236

Zentralblatt MATH identifier
1012.62098

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60G18: Self-similar processes

Keywords
Long range dependence unknown pole

Citation

Giraitis, L.; Hidalgo, J.; Robinson, P. M. Gaussian estimation of parametric spectral density with unknown pole. Ann. Statist. 29 (2001), no. 4, 987--1023. doi:10.1214/aos/1013699989. https://projecteuclid.org/euclid.aos/1013699989


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