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**Klüppelberg, Claudia and Lindner, A. (2005): Extreme value theory for moving average processes with light-tailed innovations. Collaborative Research Center 386, Discussion Paper 432 [PDF, 400kB]**

## Abstract

We consider stationary infinite moving average processes of the form $Y_n = \sum c_i Z_{n+i}$, where the sum ranges over the integers, (Z_i) is a sequence of iid random variables with ``light tails'' and (c_i) is a sequence of positive and summable coefficients. By light tails we mean that Z_0 has a bounded density $f(t)$ behaving asymptotically like $v(t) \exp (-g(t) )$, where v(t) behaves roughly like a constant as t goes to infinity, and g(t) is strictly convex satisfying certain asymptotic regularity conditions. We show that the iid sequence associated with Y_0 is in the maximum domain of attraction of the Gumbel distribution. Under additional regular variation conditions on g, it is shown that the stationary sequence (Y_n) has the same extremal behaviour as its associated iid sequence. This generalizes results of Rootz\'en (1986, 1987), where $g(t) = t^p$ and $v(t)=c t^d$ for p > 1, positive c and a real constant d.

Item Type: | Paper |
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Faculties: | Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386 Special Research Fields > Special Research Field 386 |

Subjects: | 500 Science > 510 Mathematics |

URN: | urn:nbn:de:bvb:19-epub-1801-4 |

Language: | English |

Item ID: | 1801 |

Date Deposited: | 11. Apr 2007 |

Last Modified: | 04. Nov 2020, 12:45 |