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

Scotto, Manuel; Ferreira, Helena

Applied Stochastic Models in Business and Industry, 19(4) (2003), 303-313

Let {Xk}k?1 be a strictly stationary time series. For a strictly increasing sampling function g:?[RIGHTWARDS ARROW]? 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.