Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

Extremes of deterministic sub‐sampled moving averages with heavy‐tailed innovations 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Stochastic Models in Business and Industry Wiley

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

Download PDF
11 pages

Loading next page...
 
/lp/wiley/extremes-of-deterministic-sub-sampled-moving-averages-with-heavy-epjOxrJnWl

References (10)

Publisher
Wiley
Copyright
Copyright © 2003 John Wiley & Sons, Ltd.
ISSN
1524-1904
eISSN
1526-4025
DOI
10.1002/asmb.500
Publisher site
See Article on Publisher Site

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.

Journal

Applied Stochastic Models in Business and Industry – Wiley

Published: Oct 1, 2003

There are no references for this article.