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On the Maximum of a Bivariate Max-INAR(1) Process

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Recent Developments in Statistics and Data Science (SPE 2021)

Abstract

In this paper, we introduce a \(\mathbb {Z}_+^2\)-valued strictly stationary bivariate max-INAR(1) model, which is an extension of the univariate max-INAR(1) model, introduced and studied in [1]. We consider that the marginals have a double geometric distribution in the sense of Marshall and Olkin [2]. As a consequence, we deduce that the innovations have a tail equivalent to a bivariate geometric distribution. By proving that the restriction dependence conditions introduced in [3] hold, we establish asymptotic lower and upper bounds for the distribution function of the double maxima.

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Acknowledgements

The authors would like to thank the reviewer for his/her useful comments and suggestions.

The work of the first author was partially supported by Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, University of Lisbon—UIDB/04621/2020, funded by the Portuguese Government through FCT/MCTES. The work of the second author was partially supported by the Centre for Mathematics of the University of Coimbra—UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES.

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Correspondence to Sandra Dias .

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Dias, S., da Graça Temido, M. (2022). On the Maximum of a Bivariate Max-INAR(1) Process. In: Bispo, R., Henriques-Rodrigues, L., Alpizar-Jara, R., de Carvalho, M. (eds) Recent Developments in Statistics and Data Science. SPE 2021. Springer Proceedings in Mathematics & Statistics, vol 398. Springer, Cham. https://doi.org/10.1007/978-3-031-12766-3_5

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