Sensivity of the Hermite rank
Statistics Theory
2018-01-09 v2 Statistics Theory
Abstract
The Hermite rank appears in limit theorems involving long memory. We show that an Hermite rank higher than one is unstable when the data is slightly perturbed by transformations such as shift and scaling. We carry out a "near higher order rank analysis" to illustrate how the limit theorems are affected by a shift perturbation that is decreasing in size. As a byproduct of our analysis, we also prove the coincidence of the Hermite rank and the power rank in the Gaussian context. The paper is a technical companion of \citet{bai:taqqu:2017:instability} which discusses the instability of the Hermite rank in the statistical context. (Older title "Some properties of the Hermite rank">)
Keywords
Cite
@article{arxiv.1710.01612,
title = {Sensivity of the Hermite rank},
author = {Shuyang Bai and Murad s. Taqqu},
journal= {arXiv preprint arXiv:1710.01612},
year = {2018}
}