IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v27y2025i2d10.1007_s11009-025-10162-w.html
   My bibliography  Save this article

The Uniform Poisson–Ailamujia INAR(1) Process with Random Coefficient

Author

Listed:
  • M. R. Irshad

    (Cochin University of Science and Technology)

  • Muhammed Ahammed

    (Cochin University of Science and Technology)

  • R. Maya

    (Cochin University of Science and Technology)

Abstract

Count data modeling is a critical aspect across various disciplines. However, traditional models, such as first-order integer-valued autoregressive processes, often struggle to capture the inherent variability in real-world scenarios. The incorporation of a randomized thinning operator in the first-order integer-valued autoregressive process addresses these limitations. This paper introduces a novel stationary first-order integer-valued autoregressive process with a random coefficient having uniform Poisson–Ailamujia distributed marginals. This process encompasses the first-order integer-valued autoregressive process with binomial thinning as a particular case. The paper presents a comprehensive exploration of the statistical properties of the process. Furthermore, we explore distinct parameter estimation approaches and forecasting methods, enhancing the modeling capabilities of the process, with performance evaluation conducted through a simulation study. The study concludes with a comparative analysis and practical application of the proposed model to real-world data, validating its adaptability and potential across diverse applications in the context of the first-order integer-valued autoregressive process with a random coefficient.

Suggested Citation

  • M. R. Irshad & Muhammed Ahammed & R. Maya, 2025. "The Uniform Poisson–Ailamujia INAR(1) Process with Random Coefficient," Methodology and Computing in Applied Probability, Springer, vol. 27(2), pages 1-20, June.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:2:d:10.1007_s11009-025-10162-w
    DOI: 10.1007/s11009-025-10162-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-025-10162-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-025-10162-w?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Bu, Ruijun & McCabe, Brendan, 2008. "Model selection, estimation and forecasting in INAR(p) models: A likelihood-based Markov Chain approach," International Journal of Forecasting, Elsevier, vol. 24(1), pages 151-162.
    3. Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
    4. 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.
    5. Radhakumari Maya & Christophe Chesneau & Anuresha Krishna & Muhammed Rasheed Irshad, 2022. "Poisson Extended Exponential Distribution with Associated INAR(1) Process and Applications," Stats, MDPI, vol. 5(3), pages 1-18, August.
    6. Ruijun Bu & Brendan McCabe & Kaddour Hadri, 2008. "Maximum likelihood estimation of higher‐order integer‐valued autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 973-994, November.
    7. 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.
    8. Emrah Altun & Naushad Mamode Khan, 2022. "Modelling with the Novel INAR(1)-PTE Process," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1735-1751, September.
    9. Wagner Barreto-Souza, 2015. "Zero-Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 839-852, November.
    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. M. R. Irshad & Muhammed Ahammed & R. Maya, 2025. "Monitoring mean of INAR(1) process with discrete mixture exponential innovations," Computational Statistics, Springer, vol. 40(2), pages 821-862, February.
    2. Wagner Barreto-Souza, 2019. "Mixed Poisson INAR(1) processes," Statistical Papers, Springer, vol. 60(6), pages 2119-2139, December.
    3. Robert Jung & A. Tremayne, 2011. "Useful models for time series of counts or simply wrong ones?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(1), pages 59-91, March.
    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. Axel Groß‐KlußMann & Nikolaus Hautsch, 2013. "Predicting Bid–Ask Spreads Using Long‐Memory Autoregressive Conditional Poisson Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(8), pages 724-742, December.
    6. Jian Pei & Yang Lu, 2025. "Forecasting natural disaster frequencies using nonstationary count time series models," Statistical Papers, Springer, vol. 66(3), pages 1-44, April.
    7. Brajendra C. Sutradhar, 2008. "On forecasting counts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(2), pages 109-129.
    8. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    9. repec:hum:wpaper:sfb649dp2011-044 is not listed on IDEAS
    10. Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics 0839, Faculty of Economics, University of Cambridge.
    11. Brannas, Kurt, 1995. "Prediction and control for a time-series count data model," International Journal of Forecasting, Elsevier, vol. 11(2), pages 263-270, June.
    12. Snyder, Ralph D. & Ord, J. Keith & Beaumont, Adrian, 2012. "Forecasting the intermittent demand for slow-moving inventories: A modelling approach," International Journal of Forecasting, Elsevier, vol. 28(2), pages 485-496.
    13. Youn Ahn, Jae & Jeong, Himchan & Lu, Yang, 2021. "On the ordering of credibility factors," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 626-638.
    14. HEINEN, Andréas, 2003. "Modelling time series count data: an autoregressive conditional Poisson model," LIDAM Discussion Papers CORE 2003062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Nobuhiko Terui & Masataka Ban, 2013. "Multivariate Time Series Model with Hierarchical Structure for Over-dispersed Discrete Outcomes," TMARG Discussion Papers 113, Graduate School of Economics and Management, Tohoku University, revised Aug 2013.
    16. Harvey, Andrew, 2010. "Tracking a changing copula," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 485-500, June.
    17. Svetunkov, Ivan & Boylan, John E., 2023. "iETS: State space model for intermittent demand forecasting," International Journal of Production Economics, Elsevier, vol. 265(C).
    18. Shang, Zuofeng, 2012. "On latent process models in multi-dimensional space," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1259-1266.
    19. 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.
    20. Ki Hong Kim & Young Jae Han & Sugil Lee & Sung Won Cho & Chulung Lee, 2019. "Text Mining for Patent Analysis to Forecast Emerging Technologies in Wireless Power Transfer," Sustainability, MDPI, vol. 11(22), pages 1-24, November.
    21. Ord, J. Keith & Koehler, Anne B. & Snyder, Ralph D. & Hyndman, Rob J., 2009. "Monitoring processes with changing variances," International Journal of Forecasting, Elsevier, vol. 25(3), pages 518-525, July.

    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:metcap:v:27:y:2025:i:2:d:10.1007_s11009-025-10162-w. 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.