# Extremes of periodic moving averages of random variables with regularly varying tail probabilities.

SORT (2004)

• Volume: 28, Issue: 2, page 161-176
• ISSN: 1696-2281

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## Abstract

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We define a family of local mixing conditions that enable the computation of the extremal index of periodic sequences from the joint distributions of k consecutive variables of the sequence. By applying results, under local and global mixing conditions, to the (2m - 1)-dependent periodic sequence Xn(m) = Σj=-mm-1 cjZn-j, n ≥ 1, we compute the extremal index of the periodic moving average sequence Xn = Σj=-∞∞ cjZn-j, n ≥ 1, of random variables with regularly varying tail probabilities.This paper generalizes the theory for extremes of stationary moving averages with regularly varying tail probabilities.

## How to cite

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Martins, Ana Paula, and Ferreira, Helena. "Extremes of periodic moving averages of random variables with regularly varying tail probabilities.." SORT 28.2 (2004): 161-176. <http://eudml.org/doc/40456>.

@article{Martins2004,
abstract = {We define a family of local mixing conditions that enable the computation of the extremal index of periodic sequences from the joint distributions of k consecutive variables of the sequence. By applying results, under local and global mixing conditions, to the (2m - 1)-dependent periodic sequence Xn(m) = Σj=-mm-1 cjZn-j, n ≥ 1, we compute the extremal index of the periodic moving average sequence Xn = Σj=-∞∞ cjZn-j, n ≥ 1, of random variables with regularly varying tail probabilities.This paper generalizes the theory for extremes of stationary moving averages with regularly varying tail probabilities.},
author = {Martins, Ana Paula, Ferreira, Helena},
journal = {SORT},
keywords = {Procesos estocásticos; Series temporales; Teoría de valores extremos; periodic moving average processes; extremal index; mixing condition},
language = {eng},
number = {2},
pages = {161-176},
title = {Extremes of periodic moving averages of random variables with regularly varying tail probabilities.},
url = {http://eudml.org/doc/40456},
volume = {28},
year = {2004},
}

TY - JOUR
AU - Martins, Ana Paula
AU - Ferreira, Helena
TI - Extremes of periodic moving averages of random variables with regularly varying tail probabilities.
JO - SORT
PY - 2004
VL - 28
IS - 2
SP - 161
EP - 176
AB - We define a family of local mixing conditions that enable the computation of the extremal index of periodic sequences from the joint distributions of k consecutive variables of the sequence. By applying results, under local and global mixing conditions, to the (2m - 1)-dependent periodic sequence Xn(m) = Σj=-mm-1 cjZn-j, n ≥ 1, we compute the extremal index of the periodic moving average sequence Xn = Σj=-∞∞ cjZn-j, n ≥ 1, of random variables with regularly varying tail probabilities.This paper generalizes the theory for extremes of stationary moving averages with regularly varying tail probabilities.
LA - eng
KW - Procesos estocásticos; Series temporales; Teoría de valores extremos; periodic moving average processes; extremal index; mixing condition
UR - http://eudml.org/doc/40456
ER -

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