Stochastic Environmental Research and Risk Assessment

, Volume 32, Issue 9, pp 2495–2514 | Cite as

A full ARMA model for counts with bounded support and its application to rainy-days time series

  • Sónia Gouveia
  • Tobias A. Möller
  • Christian H. Weiß
  • Manuel G. Scotto
Original Paper


Motivated by a large dataset containing time series of weekly number of rainy days collected over two thousand locations across Europe and Russia for the period 2000–2010, we propose a new class of ARMA-like model for time series of bounded counts, which can also handle extra-binomial variation. We abbreviate this model as bvARMA, as it is based upon a novel operation referred to as binomial variation. After having discussed important stochastic properties and proposed a model-fitting approach relying on maximum likelihood estimation, we apply the bvARMA model family to the rainy-days time series. Results show that both bvAR and bvMA models are adequate and exhibit a similar performance. Furthermore, bvARMA results outperform those obtained by fitting ordinary discrete ARMA (NDARMA) models of the same order.


Binomial variation Count time series ARMA structure Rainy-days time series 



The authors thank the Associate Editor and the referees for carefully reading the article and for their comments, which greatly improved the article.

Supplementary material


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Instituto de Engenharia Eletrónica e Informática de Aveiro (IEETA) and Centro de I&D em Matemática e Aplicações (CIDMA)Universidade de AveiroAveiroPortugal
  2. 2.Department of Mathematics and StatisticsHelmut Schmidt UniversityHamburgGermany
  3. 3.Departamento de Matemática and CEMAT, ISTUniversidade de LisboaLisboaPortugal

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