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Zero-modified count time series modeling with an application to influenza cases

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Abstract

The past few decades have seen considerable interest in modeling time series of counts, with applications in many domains. Classical and Bayesian modeling have primarily focused on conditional Poisson sampling distributions at each time. There is very little research on modeling time series involving Zero-Modified (i.e., Zero Deflated or Inflated) distributions. This paper aims to fill this gap and develop models for count time series involving Zero-Modified distributions, which belong to the Power Series family and are suitable for time series exhibiting both zero-inflation and zero-deflation. A full Bayesian approach via the Hamiltonian Monte Carlo (HMC) technique enables accurate modeling and inference. The paper illustrates our approach using time series on the number of deaths from the influenza virus in the city of São Paulo, Brazil.

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Acknowledgements

Marinho G. Andrade is supported by the Brazilian organization FAPESP (2019/21766-8); Katiane S. Conceição is supported by the Brazilian organization FAPESP (2019/22412-5).

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Author notes

  1. K. S. Conceição and N. Ravishanker have contributed equally to this work.

Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, University of São Paulo, São Carlos, São Paulo, 13566-590, Brazil

    Marinho G. Andrade & Katiane S. Conceição

  2. Department of Statistics, University of Connecticut, Storrs, Connecticut, 06269, USA

    Nalini Ravishanker

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  1. Marinho G. Andrade
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  3. Nalini Ravishanker
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All authors contributed to the study conception and design. All authors read and approved the final manuscript.

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Correspondence to Marinho G. Andrade.

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Andrade, M.G., Conceição, K.S. & Ravishanker, N. Zero-modified count time series modeling with an application to influenza cases. AStA Adv Stat Anal (2023). https://doi.org/10.1007/s10182-023-00488-6

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