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Multivariate extreme values in T-periodic random sequences under mild oscillation restrictions

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  • Ferreira, Helena

Abstract

If the sequence of partial maxima, generated by a multivariate T-periodic sequence {Xn = (Xn1, ..., Xnd)}n [greater-or-equal, slanted] 1, under an appropriate mixing condition, converges in distribution, under linear normalization, then the limit is a multivariate extreme value distribution. Sufficient conditions for the limiting independence of the components and existence of the multivariate extremal index are given. Limiting results for exceedance counts can be easily obtained from exceedance runs of {Xnj}n [greater-or-equal, slanted] 1, J = 1, ..., d.

Suggested Citation

  • Ferreira, Helena, 1994. "Multivariate extreme values in T-periodic random sequences under mild oscillation restrictions," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 111-125, January.
    • Handle: RePEc:eee:spapps:v:49:y:1994:i:1:p:111-125
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    Cited by:

    1. A. P. Martins & J. R. Sebastião, 2019. "Methods for estimating the upcrossings index: improvements and comparison," Statistical Papers, Springer, vol. 60(4), pages 1317-1347, August.
    2. Marta Ferreira & Helena Ferreira, 2013. "Extremes of multivariate ARMAX processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 606-627, November.
    3. Ferreira, Helena & Ferreira, Marta, 2015. "Extremes of scale mixtures of multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 82-99.
    4. Helena Ferreira & Ana Paula Martins & Maria Graça Temido, 2021. "Extremal behaviour of a periodically controlled sequence with imputed values," Statistical Papers, Springer, vol. 62(6), pages 2991-3013, December.

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