Resumen de Extremes of periodic moving averages of random variables with regularly varying tail probabilities

Helena Ferreira, Ana Paula Martins Bialer

• català

  Definim una fam¿ilia de condicions de mixtura locals que permeten el c`alcul de l'¿index extremal de successions peri`odiques a partir de la distribuci¿o conjunta de k variables consecutives de la successi¿o. Aplicant els resultats, sota condicions de mixtura locals i globals, a la successi¿o peri`odica (2m - 1)-dependent X(m) n = _m-1 j=-m cj Zn-j, n _ 1, calculem l'¿index extremal de la successi¿o peri`odica Xn = _8j=-8 cj Zn-j, n _ 1, de variables aleat`ories amb probabilitats de les cues de variaci¿o regular. Aquest article generalitza la teoria d'extrems de mitjanes m`obils estacion`aries amb probabilitats de les cues de variaci¿o regular.

• English

  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 X(m) n = _m-1 j=-m cj Zn-j, n _ 1, we compute the extremal index of the periodic moving average sequence Xn = _8j=-8 cj Zn-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.