Research Article
Extremes of deterministic sub‐sampled moving averages with heavy‐tailed innovations
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.
Citing Literature
Number of times cited according to CrossRef: 5
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