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A flexible INAR(1) time series model with dependent zero-inflated count series and medical contagious cases

Author

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  • Shirozhan, M.
  • Bakouch, Hassan S.
  • Mohammadpour, M.

Abstract

In order to understand the behavior of disease transmission and develop better policies to overcome the problem, time series modeling and forecasting of infectious diseases are crucial. Therefore, a flexible INAR(1) time series model based on dependent zero-inflated count series is proposed. A flexible discrete distribution is considered for innovation terms of the process with some interesting behavior. Some statistical properties of the proposed INAR(1) time series model are provided, and its interpretation of contagious diseases is represented. The unknown parameters of the proposed process are estimated through several estimation methods. The efficiency of the estimates is evaluated by the Monte Carlo simulation approach. Fitting, modeling and analyzing some recent contagious cases are investigated, namely the weekly counts of Hantavirus, Chickenpox and Tuberculosis diseases. The earlier data sets forecasts are investigated under coherent procedures, including the median and modified Sieve bootstrap approaches.

Suggested Citation

  • Shirozhan, M. & Bakouch, Hassan S. & Mohammadpour, M., 2023. "A flexible INAR(1) time series model with dependent zero-inflated count series and medical contagious cases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 216-230.
    • Handle: RePEc:eee:matcom:v:206:y:2023:i:c:p:216-230
    DOI: 10.1016/j.matcom.2022.11.014
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    References listed on IDEAS

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    1. Annika Homburg & Christian H. Weiß & Layth C. Alwan & Gabriel Frahm & Rainer Göb, 2019. "Evaluating Approximate Point Forecasting of Count Processes," Econometrics, MDPI, vol. 7(3), pages 1-28, July.
    2. Shengqi Tian & Dehui Wang & Shuai Cui, 2020. "A seasonal geometric INAR process based on negative binomial thinning operator," Statistical Papers, Springer, vol. 61(6), pages 2561-2581, December.
    3. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 407-417, October.
    4. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
    5. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 422-422, October.
    6. M. S. Eliwa & M. El-Morshedy, 2022. "A one-parameter discrete distribution for over-dispersed data: statistical and reliability properties with applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(10), pages 2467-2487, July.
    7. Borges, Patrick & Molinares, Fabio Fajardo & Bourguignon, Marcelo, 2016. "A geometric time series model with inflated-parameter Bernoulli counting series," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 264-272.
    8. Lorenzo Pascual & Juan Romo & Esther Ruiz, 2004. "Bootstrap predictive inference for ARIMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 449-465, July.
    9. Nisreen Shamma & Mehrnaz Mohammadpour & Masoumeh Shirozhan, 2020. "A time series model based on dependent zero inflated counting series," Computational Statistics, Springer, vol. 35(4), pages 1737-1757, December.
    10. Robert C. Jung & A. R. Tremayne, 2011. "Convolution‐closed models for count time series with applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(3), pages 268-280, May.
    11. Aleksandar S. Nastić & Miroslav M. Ristić & Ana V. Miletić Ilić, 2017. "A geometric time-series model with an alternative dependent Bernoulli counting series," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(2), pages 770-785, January.
    12. M. A. Al‐Osh & A. A. Alzaid, 1987. "First‐Order Integer‐Valued Autoregressive (Inar(1)) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 261-275, May.
    13. Raju Maiti & Atanu Biswas, 2015. "Coherent forecasting for stationary time series of discrete data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 337-365, July.
    14. A. Alzaid & M. Al‐Osh, 1988. "First‐Order Integer‐Valued Autoregressive (INAR (1)) Process: Distributional and Regression Properties," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 42(1), pages 53-61, March.
    15. A. Alzaid & M. Al-Osh, 1993. "Some autoregressive moving average processes with generalized Poisson marginal distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 223-232, June.
    16. Jung, Robert C. & Tremayne, A.R., 2006. "Coherent forecasting in integer time series models," International Journal of Forecasting, Elsevier, vol. 22(2), pages 223-238.
    17. Miroslav M. Ristić & Aleksandar S. Nastić & Ana V. Miletić Ilić, 2013. "A geometric time series model with dependent Bernoulli counting series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 466-476, July.
    18. Ana V. Miletić Ilić, 2016. "A geometric time series model with a new dependent Bernoulli counting series," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(21), pages 6400-6415, November.
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