Authors : Enesi Latifat Oyiza; Shobanke Dolapo; Paul Otaru; Benson Onoghojobi; Babatunde O. R.

Volume/Issue : Volume 11 - 2026, Issue 2 - February

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Google Scholar : https://tinyurl.com/43dwx6b9

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DOI : https://doi.org/10.38124/ijisrt/26feb393

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Abstract : The Delaporte-DCINMA(q) model is a novel integer-valued moving average procedure for overdispersed count time series that is presented in this study. The model preserves discreteness through binomial thinning while overcoming the equidispersion limitation of Poisson-based models by utilizing Delaporte-distributed innovations. We establish the moment structures and important statistical features of the model. Simulation studies show the finite-sample performance and consistency of the estimator. The model's practical usefulness is confirmed by an application to U.S. polio death data, which effectively captures both considerable serial dependence and overdispersion. A versatile and reliable framework for examining correlated count data from a variety of disciplines is offered by the suggested model.

Keywords : Generalized Method of Moments (GMM), Delaporte Distribution, DCINMA Model, Overdispersion, and Integer-Valued Time Series.

References :

1. H. Steutel and K. van Harn, Discrete Analogues of Self-Decomposability and Stability, Ann. Probab., vol. 7, no. 5, pp. 893–899, 1979.
2. C. H. Weiß, An Introduction to Discrete-Valued Time Series, Weinheim, Germany: Wiley-VCH, 2018.
3. K. Yu and H. Wang, “A new overdispersed integer-valued moving average model with dependent counting series,” Entropy, vol. 23, no. 6, p. 706, 2021.
4. M. Al-Osh and A. Alzaid, “First-order integer-valued autoregressive (INAR(1)) process with generalized innovations,” J. Time Series Anal., vol. 8, pp. 261–275, 1987.
5. R. A. Rigby, D. M. Stasinopoulos, and C. Akantziliotou, “A framework for modelling overdispersed count data, including the Poisson-shifted generalized inverse Gaussian distribution,” Comput. Stat. Data Anal., vol. 53, no. 2, pp. 381–393, 2008.
6. A. Adler, “Delaporte Distribution Functions for R,” CRAN R Package ‘Delaporte’, 2017. [Online]. Available: https://cran.r-project.org/package=Delaporte
7. M. McKenzie, “Some simple models for discrete variate time series,” Water Resour. Bull., vol. 21, no. 4, pp. 645–650, 1985.
8. H. Alzaid and M. Al-Osh, “An integer-valued moving average (INMA) process,” J. Appl. Probab., vol. 25, pp. 314–324, 1988.
9. P. Consul and G. Jain, “A generalization of the Poisson distribution,” Technometrics, vol. 15, no. 4, pp. 791–799, 1973.
10. J. Fokianos, “Count time series models,” in Handbook of Statistics, vol. 41, Elsevier, 2019, pp. 403–430.
11. C. H. Weiß, “Thinning operations for modeling time series of counts—a survey,” AStA Advances in Statistical Analysis, vol. 95, pp. 319–341, 2011.
12. C. H. Weiß, “Serial dependence and overdispersion in count data: models, estimation, and diagnostics,” Statistical Modelling, vol. 19, no. 3, pp. 231–256, 2019.
13. K. Yu and H. Wang, “A dependent counting integer-valued time series model,” Entropy, vol. 24, no. 4, p. 546, 2022.
14. G. E. Taufer and J. C. R. Teixeira, “Parameter estimation for integer-valued autoregressive models using the GMM approach,” Stat. Papers, vol. 57, pp. 725–743, 2016.