Sensitivity of the Hermite rank

Shuyang Bai and Murad S. Taqqu

Stochastic Processes and their Applications, 2019, vol. 129, issue 3, 822-840

Abstract: 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.

Keywords: Long-range dependence; Long memory; Hermite rank; Power rank; Limit theorem; Instability (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2018.03.020

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