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Extremes of integer-valued moving average sequences

Abstract

This paper aims to analyze the extremal properties of integer-valued moving average sequences obtained as discrete analogues of conventional moving averages replacing scalar multiplication by binomial thinning. In particular, we consider the case in which the scalar coefficients are replaced by random coefficients since in real applications the thinning probabilities may depend on several factors changing in time. Furthermore, the extremal behavior of periodic integer-valued moving average sequences is also considered. In this case, we find that, when assessing their clustering tendency of high-threshold exceedances, the extremal index is the same as for the stationary case.

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Correspondence to Andreia Hall.

Additional information

Research (partially) supported by Unidade de Investigação Matemática e Aplicações of Universidade de Aveiro through Programa Operacional “Ciência, Tecnologia, Inovação” of the Fundação para a Ciência e a Tecnologia (FCT) cofinanced by the European Community fund FEDER. The second author is also supported by the project PTDC/MAT/64353/2006.

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Hall, A., Scotto, M. & Cruz, J. Extremes of integer-valued moving average sequences. TEST 19, 359–374 (2010). https://doi.org/10.1007/s11749-009-0158-6

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  • DOI: https://doi.org/10.1007/s11749-009-0158-6

Keywords

  • Extreme value theory
  • Binomial thinning
  • Extremal index
  • Integer-valued sequences

Mathematics Subject Classification (2000)

  • 60G70