id: 05732039
dt: j
an: 05732039
au: Faÿ, Gilles
ti: Moment bounds for non-linear functionals of the periodogram.
so: Stochastic Processes Appl. 120, No. 6, 983-1009 (2010).
py: 2010
pu: Elsevier Science Publishers B.V. (North-Holland), Amsterdam
la: EN
cc: 
ut: linear processes; discrete Fourier transform; periodogram; long range
    dependence; Geweke and Porter-Hudak (GPH) estimator; log-periodogram
    regression
ci: Zbl 0534.62062; Zbl 0870.62073
li: doi:10.1016/j.spa.2010.02.007
ab: Summary: We prove the validity of Edgeworth expansions of discrete Fourier
    transforms of some linear time series. This result is applied to
    approach moments of nonlinear functionals of the periodogram. As an
    illustration, we give an expression of the mean square error of the
    slightly modified {\it J. Geweke} and {\it S. Porter-Hudak} estimator
    [J. Time Ser. Anal. 4, 221‒238 (1983; Zbl 0534.62062)] of the long
    memory parameter. We prove that this estimator is rate optimal,
    extending a result of {\it L. Giraitis} et al. [ibid. 18, No.~1,
    49‒60 (1997; Zbl 0870.62073)] from Gaussian to linear processes.
rv: