Extremes of multivariate ARMAX processes

• Marta Ferreira ^[2] ; Helena Ferreira ^[1]
  1. [1] Universidade da Beira Interior

     Universidade da Beira Interior

     Covilhã (Conceição), Portugal

     
  2. [2] Minho University/DMA
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 22, Nº. 4, 2013, págs. 606-627
• Idioma: inglés
• DOI: 10.1007/s11749-013-0326-6
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.