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Extremes of sub-sampled integer-valued moving average models with heavy-tailed innovations

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  • Hall, A.
  • Scotto, M. G.

Abstract

Let {Xk} be a non-negative integer-valued stationary moving average sequence and define Yk=XTk as the sub-sampled series at a fixed integer interval T>1. We look at the limiting distribution of sample maxima of {Yk} and the corresponding extremal index.

Suggested Citation

  • Hall, A. & Scotto, M. G., 2003. "Extremes of sub-sampled integer-valued moving average models with heavy-tailed innovations," Statistics & Probability Letters, Elsevier, vol. 63(1), pages 97-105, May.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:1:p:97-105
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    References listed on IDEAS

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    1. M. G. Scotto & K. F. Turkman & C. W. Anderson, 2003. "Extremes of Some Sub‐Sampled Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 579-590, September.
    2. M. E. Robinson & J. A. Tawn, 2000. "Extremal analysis of processes sampled at different frequencies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 117-135.
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    Cited by:

    1. Paolo Gorgi, 2020. "Beta–negative binomial auto‐regressions for modelling integer‐valued time series with extreme observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1325-1347, December.
    2. J. Hüsler & M. G. Temido & A. Valente-Freitas, 2022. "On the Maximum of a Bivariate INMA Model with Integer Innovations," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2373-2402, December.
    3. Scotto, M., 2005. "Extremes of a class of deterministic sub-sampled processes with applications to stochastic difference equations," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 417-434, March.

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