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Extremes of deterministic sub‐sampled moving averages with heavy‐tailed innovations

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  • M. Scotto
  • H. Ferreira

Abstract

Let {Xk}k⩾1 be a strictly stationary time series. For a strictly increasing sampling function g:ℕ→ℕ define Yk=Xg(k) as the deterministic sub‐sampled time series. In this paper, the extreme value theory of {Yk} is studied when Xk has representation as a moving average driven by heavy‐tailed innovations. Under mild conditions, convergence results for a sequence of point processes based on {Yk} are proved and extremal properties of the deterministic sub‐sampled time series are derived. In particular, we obtain the limiting distribution of the maximum and the corresponding extremal index. Copyright © 2003 John Wiley & Sons, Ltd.

Suggested Citation

  • M. Scotto & H. Ferreira, 2003. "Extremes of deterministic sub‐sampled moving averages with heavy‐tailed innovations," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 19(4), pages 303-313, October.
    • Handle: RePEc:wly:apsmbi:v:19:y:2003:i:4:p:303-313
    DOI: 10.1002/asmb.500
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