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Sensitivity of the Hermite rank. (English) Zbl 1412.62114

Summary: 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 S. Bai and M. S. Taqqu [Stat. Sci. 33, No. 1, 96–116 (2018; Zbl 1407.62274)] which discusses the instability of the Hermite rank in the statistical context.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60F05 Central limit and other weak theorems

Citations:

Zbl 1407.62274

Software:

longmemo
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Full Text: DOI arXiv

References:

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