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

• Autores: Helena Ferreira, Ana Paula Martins Bialer
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 28, Nº. 2, 2004, págs. 161-176
• Idioma: inglés
• Títulos paralelos:
  • Extremos de medias móviles periódicas de variables aleatorias con probabilidades de cola de variación regular.
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• Resumen
  • 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.