  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.
