, Volume 22, Issue 4, pp 606–627

Extremes of multivariate ARMAX processes

Original Paper

DOI: 10.1007/s11749-013-0326-6

Cite this article as:
Ferreira, M. & Ferreira, H. TEST (2013) 22: 606. doi:10.1007/s11749-013-0326-6


We define a new multivariate time series model by generalizing the ARMAX process in a multivariate way. We give conditions on stationarity and analyze local dependence and domains of attraction. As a consequence of the obtained results, we derive new multivariate extreme value distributions. We characterize the extremal dependence by computing the multivariate extremal index and bivariate upper tail dependence coefficients. An estimation procedure for the multivariate extremal index is presented. We also address the marginal estimation and propose a new estimator for the ARMAX autoregressive parameter.


Multivariate extreme value theory Maximum autoregressive processes Multivariate extremal index Tail dependence Asymptotic independence 

Mathematics Subject Classification


Copyright information

© Sociedad de Estadística e Investigación Operativa 2013

Authors and Affiliations

  1. 1.Center of MathematicsMinho University/DMABragaPortugal
  2. 2.Department of MathematicsUniversity of Beira InteriorCovilhãPortugal

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