, Volume 22, Issue 4, pp 606–627 | Cite as

Extremes of multivariate ARMAX processes

  • Marta Ferreira
  • Helena Ferreira
Original Paper


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




We are very grateful to the referees for their valuable corrections and suggestions. Helena Ferreira was partially supported by the research unit “Centro de Matemática” of the University of Beira Interior and the research project PTDC/MAT/108575/2008 through the Foundation for Science and Technology (FCT) co-financed by FEDER/COMPETE. Marta Ferreira was financed by FEDER Funds through “Programa Operacional Factores de Competitividade—COMPETE” and by Portuguese Funds through FCT—“Fundação para a Ciência e a Tecnologia”, within the Project Est-C/MAT/UI0013/2011.


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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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