Moment bounds for non-linear functionals of the periodogram

G. Faÿ 1
1 APC - ADAMIS
LPP - Laboratoire Paul Painlevé, APC - UMR 7164 - AstroParticule et Cosmologie, MAS - Mathématiques Appliquées aux Systèmes - EA 4037
Abstract : 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.
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Journal articles
Stochastic Processes and their Applications, Elsevier, 2010, 120, pp.983-1009. <10.1016/j.spa.2010.02.007>


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Submitted on : Tuesday, October 14, 2008 - 12:00:13 PM
Last modification on : Tuesday, October 28, 2014 - 6:00:17 PM

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G. Faÿ. Moment bounds for non-linear functionals of the periodogram. Stochastic Processes and their Applications, Elsevier, 2010, 120, pp.983-1009. <10.1016/j.spa.2010.02.007>. <in2p3-00330398>

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