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Extremes of deterministic sub‐sampled moving averages with heavy‐tailed innovations
Author(s) -
Scotto M.,
Ferreira H.
Publication year - 2003
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.500
Subject(s) - series (stratigraphy) , mathematics , extreme value theory , sequence (biology) , limiting , moving average , convergence (economics) , sampling (signal processing) , value (mathematics) , stationary sequence , distribution (mathematics) , combinatorics , generalized extreme value distribution , function (biology) , representation (politics) , statistical physics , statistics , stochastic process , mathematical analysis , computer science , physics , economics , filter (signal processing) , law , economic growth , engineering , genetics , biology , paleontology , evolutionary biology , political science , computer vision , mechanical engineering , politics
Let {X k } k⩾1 be a strictly stationary time series. For a strictly increasing sampling function g:ℕ→ℕ define Y k =X g(k) as the deterministic sub‐sampled time series. In this paper, the extreme value theory of {Y k } is studied when X k has representation as a moving average driven by heavy‐tailed innovations. Under mild conditions, convergence results for a sequence of point processes based on {Y k } 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.