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Stochastic Processes and their Applications 120 (2010) 983-1009
Moment bounds for non-linear functionals of the periodogram
G. Faÿ1, 2, 3

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.
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
2 :  LPP - Laboratoire Paul Painlevé
3 :  MAS - Mathématiques Appliquées aux Systèmes - EA 4037

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