IDEAS home Printed from https://ideas.repec.org/a/spr/jstada/v8y2021i1d10.1186_s40488-021-00115-2.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1186/s40488-021-00115-2
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1186/s40488-021-00115-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Hilbe,Joseph M., 2014. "Modeling Count Data," Cambridge Books, Cambridge University Press, number 9781107611252.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Morris, Darcy Steeg & Raim, Andrew M. & Sellers, Kimberly F., 2020. "A Conway–Maxwell-multinomial distribution for flexible modeling of clustered categorical data," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    2. Seng Huat Ong & Shin Zhu Sim & Shuangzhe Liu & Hari M. Srivastava, 2023. "A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data," Stats, MDPI, vol. 6(3), pages 1-14, September.
    3. 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.
    4. 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.
    5. Kimberly F. Sellers & Tong Li & Yixuan Wu & Narayanaswamy Balakrishnan, 2021. "A Flexible Multivariate Distribution for Correlated Count Data," Stats, MDPI, vol. 4(2), pages 1-19, April.
    6. Bedbur, S. & Kamps, U., 2023. "Uniformly most powerful unbiased tests for the dispersion parameter of the Conway–Maxwell–Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 196(C).
    7. Geng, Xi & Xia, Aihua, 2022. "When is the Conway–Maxwell–Poisson distribution infinitely divisible?," Statistics & Probability Letters, Elsevier, vol. 181(C).
    8. Wooi Chen Khoo & Seng Huat Ong & Atanu Biswas, 2017. "Modeling time series of counts with a new class of INAR(1) model," Statistical Papers, Springer, vol. 58(2), pages 393-416, June.
    9. Yousung Park & Hee-Young Kim, 2012. "Diagnostic checks for integer-valued autoregressive models using expected residuals," Statistical Papers, Springer, vol. 53(4), pages 951-970, November.
    10. Rodrigues, Josemar & Bazán, Jorge L. & Suzuki, Adriano K. & Balakrishnan, Narayanaswamy, 2016. "The Bayesian restricted Conway–Maxwell-Binomial model to control dispersion in count data," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 281-288.
    11. Zeng, Xiaoqiang & Kakizawa, Yoshihide, 2022. "Bias-correction of some estimators in the INAR(1) process," Statistics & Probability Letters, Elsevier, vol. 187(C).
    12. Nastić, Aleksandar S. & Ristić, Miroslav M., 2012. "Some geometric mixed integer-valued autoregressive (INAR) models," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 805-811.
    13. Yan Cui & Qi Li & Fukang Zhu, 2020. "Flexible bivariate Poisson integer-valued GARCH model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1449-1477, December.
    14. 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.
    15. Chen, Zezhun Chen & Dassios, Angelos & Tzougas, George, 2023. "A first order binomial mixed poisson integer-valued autoregressive model with serially dependent innovations," LSE Research Online Documents on Economics 112222, London School of Economics and Political Science, LSE Library.
    16. Chen, Zezhun & Dassios, Angelos, 2022. "Cluster point processes and Poisson thinning INARMA," LSE Research Online Documents on Economics 113652, London School of Economics and Political Science, LSE Library.
    17. Johannes Ferreira & Ané van der Merwe, 2022. "A Noncentral Lindley Construction Illustrated in an INAR(1) Environment," Stats, MDPI, vol. 5(1), pages 1-19, January.
    18. Vladica S. Stojanović & Hassan S. Bakouch & Eugen Ljajko & Najla Qarmalah, 2023. "Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach," Mathematics, MDPI, vol. 11(8), pages 1-25, April.
    19. Mamode Khan Naushad & Rumjaun Wasseem & Sunecher Yuvraj & Jowaheer Vandna, 2017. "Computing with bivariate COM-Poisson model under different copulas," Monte Carlo Methods and Applications, De Gruyter, vol. 23(2), pages 131-146, June.
    20. Schatz, Michael & Wheatley, Spencer & Sornette, Didier, 2022. "The ARMA Point Process and its Estimation," Econometrics and Statistics, Elsevier, vol. 24(C), pages 164-182.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jstada:v:8:y:2021:i:1:d:10.1186_s40488-021-00115-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.