Moment bounds for non-linear functionals of the periodogram

Details Moment bounds for non-linear functionals of the periodogram Moment bounds for non-linear functionals of the periodogram

2008-07-31

arxiv.org/abs/0807.5096v1

Mathematics

Statistics Theory

Scientific paper

10.1016/j.spa.2010.02.007

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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