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On the Maximum of a Bivariate INMA Model with Integer Innovations

Author

Listed:
  • J. Hüsler

    (University of Bern)

  • M. G. Temido

    (Department of Mathematics)

  • A. Valente-Freitas

    (University of Aveiro
    University of Aveiro)

Abstract

We study the limiting behaviour of the maximum of a bivariate (finite or infinite) moving average model, based on discrete random variables. We assume that the bivariate distribution of the iid innovations belong to the Anderson’s class (Anderson, 1970). The innovations have an impact on the random variables of the INMA model by binomial thinning. We show that the limiting distribution of the bivariate maximum is also of Anderson’s class, and that the components of the bivariate maximum are asymptotically independent.

Suggested Citation

  • J. Hüsler & M. G. Temido & A. Valente-Freitas, 2022. "On the Maximum of a Bivariate INMA Model with Integer Innovations," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2373-2402, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-021-09920-3
    DOI: 10.1007/s11009-021-09920-3
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    References listed on IDEAS

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    1. Isabel Silva & Maria Eduarda Silva & Cristina Torres, 2020. "Inference for bivariate integer-valued moving average models based on binomial thinning operation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(13-15), pages 2546-2564, November.
    2. Sagitov, Serik, 2017. "Tail generating functions for extendable branching processes," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1649-1675.
    3. Hall, A. & Scotto, M. G., 2003. "Extremes of sub-sampled integer-valued moving average models with heavy-tailed innovations," Statistics & Probability Letters, Elsevier, vol. 63(1), pages 97-105, May.
    4. Hsing, Tailen, 1989. "Extreme value theory for multivariate stationary sequences," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 274-291, May.
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