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A flexible univariate moving average time-series model for dispersed count data

Author

Listed:
  • Kimberly F. Sellers

    (Georgetown University
    U.S. Census Bureau)

  • Ali Arab

    (Georgetown University)

  • Sean Melville

    (Georgetown University)

  • Fanyu Cui

    (Georgetown University)

Abstract

Al-Osh and Alzaid (1988) consider a Poisson moving average (PMA) model to describe the relation among integer-valued time series data; this model, however, is constrained by the underlying equi-dispersion assumption for count data (i.e., that the variance and the mean equal). This work instead introduces a flexible integer-valued moving average model for count data that contain over- or under-dispersion via the Conway-Maxwell-Poisson (CMP) distribution and related distributions. This first-order sum-of-Conway-Maxwell-Poissons moving average (SCMPMA(1)) model offers a generalizable construct that includes the PMA (among others) as a special case. We highlight the SCMPMA model properties and illustrate its flexibility via simulated data examples.

Suggested Citation

  • Kimberly F. Sellers & Ali Arab & Sean Melville & Fanyu Cui, 2021. "A flexible univariate moving average time-series model for dispersed count data," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-12, December.
    • Handle: RePEc:spr:jstada:v:8:y:2021:i:1:d:10.1186_s40488-021-00115-2
    DOI: 10.1186/s40488-021-00115-2
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    References listed on IDEAS

    as
    1. Hilbe,Joseph M., 2014. "Modeling Count Data," Cambridge Books, Cambridge University Press, number 9781107611252, October.
    2. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
    3. Kimberly F. Sellers & Stephen J. Peng & Ali Arab, 2020. "A Flexible Univariate Autoregressive Time‐Series Model for Dispersed Count Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(3), pages 436-453, May.
    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. 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.
    6. Li Zhu & Kimberly F. Sellers & Darcy Steeg Morris & Galit Shmueli, 2017. "Bridging the Gap: A Generalized Stochastic Process for Count Data," The American Statistician, Taylor & Francis Journals, vol. 71(1), pages 71-80, January.
    7. Kurt Brännäs & Andreia Hall, 2001. "Estimation in integer‐valued moving average models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 17(3), pages 277-291, July.
    8. Borges, Patrick & Rodrigues, Josemar & Balakrishnan, Narayanaswamy & Bazán, Jorge, 2014. "A COM–Poisson type generalization of the binomial distribution and its properties and applications," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 158-166.
    9. Kimberly F. Sellers & Andrew W. Swift & Kimberly S. Weems, 2017. "Correction to: a flexible distribution class for count data," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-1, December.
    10. Kimberly F. Sellers & Andrew W. Swift & Kimberly S. Weems, 2017. "A flexible distribution class for count data," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-21, December.
    11. 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.
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