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The difference of symmetric quantiles under long range dependence

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  • Tarr, G.
  • Weber, N.C.
  • Müller, S.

Abstract

This paper investigates two robust estimators of the scale parameter given data from a stationary, long range dependent Gaussian process. In particular the limiting distributions of the interquartile range and related τ-quantile range statistics are established. In contrast to single quantiles, the limiting distribution of the difference of two symmetric quantiles is determined by the level of dependence in the underlying process. It is shown that there is no loss of asymptotic efficiency for the τ-quantile range relative to the standard deviation under extreme long range dependence which is consistent with results found previously for other estimators of scale.

Suggested Citation

  • Tarr, G. & Weber, N.C. & Müller, S., 2015. "The difference of symmetric quantiles under long range dependence," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 144-150.
    • Handle: RePEc:eee:stapro:v:98:y:2015:i:c:p:144-150
    DOI: 10.1016/j.spl.2014.12.022
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    References listed on IDEAS

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    1. Chan, Wai-sum, 1995. "Outliers and financial time series modelling: A cautionary note," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(3), pages 425-430.
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    3. Cheolwoo Park & F�lix Hernández-Campos & Long Le & J. S. Marron & Juhyun Park & Vladas Pipiras & F. D. Smith & Richard L. Smith & Michele Trovero & Zhengyuan Zhu, 2011. "Long-range dependence analysis of Internet traffic," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1407-1433, June.
    4. Wendler, Martin, 2011. "Bahadur representation for U-quantiles of dependent data," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1064-1079, July.
    5. Céline Lévy‐Leduc & Hélène Boistard & Eric Moulines & Murad S. Taqqu & Valderio A. Reisen, 2011. "Robust estimation of the scale and of the autocovariance function of Gaussian short‐ and long‐range dependent processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 135-156, March.
    6. Wendler, Martin, 2012. "U-processes, U-quantile processes and generalized linear statistics of dependent data," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 787-807.
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