Sensivity of the Hermite rank
Taqqu, Murad S.
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Citation (published version)Shuyang Bai, Murad S Taqqu. 2019. "Sensivity of the Hermite rank." Stochastic Processes and their Applications, Volume 129, Issue 3, pp. 822 - 840. https://doi.org/10.1016/j.spa.2018.03.020
The Hermite rank appears in limit theorems involving long memory. We show that a 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. We also consider the case where the deterministic shift is replaced by centering with respect to the sample mean. The paper is a companion of Bai and Taqqu (2017) which discusses the instability of the Hermite rank in the statistical context.