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

Author

Listed:
  • Marinho G. Andrade

    (University of São Paulo)

  • Katiane S. Conceição

    (University of São Paulo)

  • Nalini Ravishanker

    (University of Connecticut)

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.

Suggested Citation

  • Marinho G. Andrade & Katiane S. Conceição & Nalini Ravishanker, 2024. "Zero-modified count time series modeling with an application to influenza cases," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 611-637, September.
    • Handle: RePEc:spr:alstar:v:108:y:2024:i:3:d:10.1007_s10182-023-00488-6
    DOI: 10.1007/s10182-023-00488-6
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    References listed on IDEAS

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    1. Kim, Sungil & Kim, Heeyoung, 2016. "A new metric of absolute percentage error for intermittent demand forecasts," International Journal of Forecasting, Elsevier, vol. 32(3), pages 669-679.
    2. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    3. M. J. Campbell, 1994. "Time Series Regression for Counts: An Investigation into the Relationship between Sudden Infant Death Syndrome and Environmental Temperature," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 157(2), pages 191-208, March.
    4. Neil Shephard, 1995. "Generalized linear autoregressions," Economics Papers 8., Economics Group, Nuffield College, University of Oxford.
    5. Dietz, Ekkehart & Bohning, Dankmar, 2000. "On estimation of the Poisson parameter in zero-modified Poisson models," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 441-459, October.
    6. Richard A. Davis & William T. M. Dunsmuir & Sarah B. Streett, 2005. "Maximum Likelihood Estimation for an Observation Driven Model for Poisson Counts," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 149-159, June.
    7. Jean-Paul Chretien & Dylan George & Jeffrey Shaman & Rohit A Chitale & F Ellis McKenzie, 2014. "Influenza Forecasting in Human Populations: A Scoping Review," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-8, April.
    8. Konstantinos Fokianos & Benjamin Kedem, 2004. "Partial Likelihood Inference For Time Series Following Generalized Linear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 173-197, March.
    9. Chen, Cathy W.S. & Lee, Sangyeol, 2016. "Generalized Poisson autoregressive models for time series of counts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 51-67.
    10. Cordeiro, Gauss M. & Andrade, Marinho G. & de Castro, Mário, 2009. "Power series generalized nonlinear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1155-1166, February.
    Full references (including those not matched with items on IDEAS)

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