Multivariate MA($\infty$) processes with heavy tails and random coefficients

Shuyan Liu (1) , Johan Segers (2)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA)

Many interesting processes share the property of multivariate regular variation. This property is equivalent to existence of the tail process introduced by B. Basrak and J. Segers \cite{Basrak09} to describe the asymptotic behavior for the extreme values of a regularly varying time series. We apply this theory to multivariate MA($\infty$) processes with random coefficients.

Mots clés: extremes; heavy tails; regular variation; tail process

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Shuyan Liu, Johan Segers. Multivariate MA($\infty$) processes with heavy tails and random coefficients. 2010. ⟨hal-00624123⟩