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

Applied Stochastic Models in Business and Industry, 19(4) (2003), 303-313
http://dx.doi.org/10.1002/asmb.500

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.