Moderate deviations for non-linear functionals and empirical spectral density of moving average processes
Probability
2007-06-13 v1 Statistics Theory
Statistics Theory
Abstract
A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random variables and the continuity, or weaker, of the spectral density of the moving average process. We also obtain the moderate deviations for the empirical spectral density, exhibiting an interesting new form of the rate function, i.e. with a correction term compared to the Gaussian rate functionnal.
Cite
@article{arxiv.math/0405521,
title = {Moderate deviations for non-linear functionals and empirical spectral density of moving average processes},
author = {Hacene Djellout and Arnaud Guillin and Liming Wu},
journal= {arXiv preprint arXiv:math/0405521},
year = {2007}
}