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Extremes of scale mixtures of multivariate time series

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  • Ferreira, Helena
  • Ferreira, Marta

Abstract

Factor models have large potential in the modeling of several natural and human phenomena. In this paper we consider a multivariate time series Yn, n≥1, rescaled through random factors Tn, n≥1, extending some scale mixture models in the literature. We analyze its extremal behavior by deriving the maximum domain of attraction and the multivariate extremal index, which leads to new ways to construct multivariate extreme value distributions. The computation of the multivariate extremal index and the characterization of the tail dependence show an interesting property of these models. More precisely, however much it is the dependence within and between factors Tn, n≥1, the extremal index of the model is unit whenever Yn, n≥1, presents cross-sectional and sequential tail independence. We illustrate with examples of thinned multivariate time series and multivariate autoregressive processes with random coefficients. An application of these latter to financial data is presented at the end.

Suggested Citation

  • Ferreira, Helena & Ferreira, Marta, 2015. "Extremes of scale mixtures of multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 82-99.
  • Handle: RePEc:eee:jmvana:v:137:y:2015:i:c:p:82-99
    DOI: 10.1016/j.jmva.2015.02.002
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    References listed on IDEAS

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    1. Anthony W. Ledford & Jonathan A. Tawn, 1997. "Modelling Dependence within Joint Tail Regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 475-499.
    2. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    3. Zhengjun Zhang, 2009. "On approximating max-stable processes and constructing extremal copula functions," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 89-114, February.
    4. 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.
    5. Saralees Nadarajah & M. Ali, 2008. "Pareto Random Variables for Hydrological Modeling," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 22(10), pages 1381-1393, October.
    6. Mladenovic, Pavle & Piterbarg, Vladimir, 2006. "On asymptotic distribution of maxima of complete and incomplete samples from stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1977-1991, December.
    7. 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.
    8. Li, Haijun, 2009. "Orthant tail dependence of multivariate extreme value distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 243-256, January.
    9. repec:bla:anzsta:v:46:y:2004:i:1:p:99-112 is not listed on IDEAS
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    Cited by:

    1. Marta Ferreira & Helena Ferreira, 2017. "Analyzing the Gaver—Lewis Pareto Process under an Extremal Perspective," Risks, MDPI, vol. 5(3), pages 1-12, June.

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