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On the asymptotic location of high values of a stationary sequence

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  • Ferreira, H.
  • Scotto, M.

Abstract

In this paper, we investigate the limiting distribution of the locations related with high values generated by a strictly stationary sequence of random variables. The main tool for this purpose is the so-called local extremes comparison lemma, which enables us to obtain the convergence in distribution of various functionals related with the location of extreme order statistics, including the location of local maxima and the joint locations of the largest order statistics. Furthermore, results about the joint asymptotic behavior of the location of the first high-level exceedance and the location of the maximum are also discussed.

Suggested Citation

  • Ferreira, H. & Scotto, M., 2002. "On the asymptotic location of high values of a stationary sequence," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 475-482, December.
    • Handle: RePEc:eee:stapro:v:60:y:2002:i:4:p:475-482
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    References listed on IDEAS

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    1. A. C. Davison & N. I. Ramesh, 2000. "Local likelihood smoothing of sample extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 191-208.
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    Cited by:

    1. Emily J. Whitehouse & David I. Harvey & Stephen J. Leybourne, 2023. "Real‐Time Monitoring of Bubbles and Crashes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(3), pages 482-513, June.
    2. Luísa Pereira, 2018. "On the Asymptotic Locations of the Largest and Smallest Extremes of a Stationary Sequence," Journal of Theoretical Probability, Springer, vol. 31(2), pages 853-866, June.
    3. David I. Harvey & Stephen J. Leybourne & Robert Sollis & A.M. Robert Taylor, 2021. "Real‐time detection of regimes of predictability in the US equity premium," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(1), pages 45-70, January.
    4. Peng, Zuoxiang & Tong, Jinjun & Weng, Zhichao, 2019. "Exceedances point processes in the plane of stationary Gaussian sequences with data missing," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 73-79.

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