Moment bounds for non-linear functionals of the periodogram

In this paper, we prove the validity of the Edgeworth expansion of the Discrete Fourier transforms of some linear time series. This result is applied to approach moments of non linear functionals of the periodogram. As an illustration, we give an expression of the mean square error of the Geweke and...

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Bibliographic Details
Published in:arXiv.org 2008-07
Main Author: Faÿ, Gilles
Format: Article
Language:English
Subjects:
Fourier transforms
Gaussian process
Parameter estimation
Online Access:Get full text
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Summary:In this paper, we prove the validity of the Edgeworth expansion of the Discrete Fourier transforms of some linear time series. This result is applied to approach moments of non linear functionals of the periodogram. As an illustration, we give an expression of the mean square error of the Geweke and Porter-Hudak estimator of the long memory parameter. We prove that this estimator is rate optimal, extending the result of Giraitis, Robinson, Samarov (1997) from Gaussian to linear processes.
ISSN:2331-8422
DOI:10.48550/arxiv.0807.5096