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Sensitivity of the Hermite rank

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  • Bai, Shuyang
  • Taqqu, Murad S.

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.

Suggested Citation

  • Bai, Shuyang & Taqqu, Murad S., 2019. "Sensitivity of the Hermite rank," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 822-840.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:3:p:822-840
    DOI: 10.1016/j.spa.2018.03.020
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    References listed on IDEAS

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    1. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    2. Shuyang Bai & Murad S. Taqqu, 2013. "Multivariate Limit Theorems In The Context Of Long-Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 717-743, November.
    3. Pipiras,Vladas & Taqqu,Murad S., 2017. "Long-Range Dependence and Self-Similarity," Cambridge Books, Cambridge University Press, number 9781107039469.
    4. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
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    Cited by:

    1. Voutilainen, Marko & Ilmonen, Pauliina & Viitasaari, Lauri & Lietzén, Niko, 2023. "Note on asymptotic behavior of spatial sign autocovariance matrices," Statistics & Probability Letters, Elsevier, vol. 192(C).

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