IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v8y2025i1p22-d1610824.html
   My bibliography  Save this article

A Flexible Bivariate Integer-Valued Autoregressive of Order (1) Model for Over- and Under-Dispersed Time Series Applications

Author

Listed:
  • Naushad Mamode Khan

    (Department of Economics and Statistics, University of Mauritius, Reduit 80835, Mauritius
    These authors contributed equally to this work.)

  • Yuvraj Sunecher

    (Department of Accounting, Finance and Economics, University of Technology Mauritius, Pointe-Aux-Sables, Port Louis 11108, Mauritius
    These authors contributed equally to this work.)

Abstract

In real-life inter-related time series, the counting responses of different entities are commonly influenced by some time-dependent covariates, while the individual counting series may exhibit different levels of mutual over- or under-dispersion or mixed levels of over- and under-dispersion. In the current literature, there is still no flexible bivariate time series process that can model series of data of such types. This paper introduces a bivariate integer-valued autoregressive of order 1 (BINAR(1)) model with COM-Poisson innovations under time-dependent moments that can accommodate different levels of over- and under-dispersion. Another particularity of the proposed model is that the cross-correlation between the series is induced locally by relating the current observation of one series with the previous-lagged observation of the other series. The estimation of the model parameters is conducted via a Generalized Quasi-Likelihood (GQL) approach. The proposed model is applied to different real-life series problems in Mauritius, including transport, finance, and socio-economic sectors.

Suggested Citation

  • Naushad Mamode Khan & Yuvraj Sunecher, 2025. "A Flexible Bivariate Integer-Valued Autoregressive of Order (1) Model for Over- and Under-Dispersed Time Series Applications," Stats, MDPI, vol. 8(1), pages 1-25, March.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:1:p:22-:d:1610824
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/8/1/22/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/8/1/22/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kimberly F. Sellers & Sharad Borle & Galit Shmueli, 2012. "The COM‐Poisson model for count data: a survey of methods and applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(2), pages 104-116, March.
    2. Dominique Lord & Srinivas Reddy Geedipally & Seth D. Guikema, 2010. "Extension of the Application of Conway‐Maxwell‐Poisson Models: Analyzing Traffic Crash Data Exhibiting Underdispersion," Risk Analysis, John Wiley & Sons, vol. 30(8), pages 1268-1276, August.
    3. Aleksandar S. Nastić & Miroslav M. Ristić & Predrag M. Popović, 2016. "Estimation in a bivariate integer-valued autoregressive process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(19), pages 5660-5678, October.
    4. Pedeli, Xanthi & Karlis, Dimitris, 2013. "Some properties of multivariate INAR(1) processes," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 213-225.
    5. Seth D. Guikema & Jeremy P. Goffelt, 2008. "A Flexible Count Data Regression Model for Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 28(1), pages 213-223, February.
    6. Saralees Nadarajah, 2009. "Useful moment and CDF formulations for the COM–Poisson distribution," Statistical Papers, Springer, vol. 50(3), pages 617-622, June.
    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. Darcy Steeg Morris & Kimberly F. Sellers, 2022. "A Flexible Mixed Model for Clustered Count Data," Stats, MDPI, vol. 5(1), pages 1-18, January.
    2. S. Hadi Khazraee & Antonio Jose Sáez‐Castillo & Srinivas Reddy Geedipally & Dominique Lord, 2015. "Application of the Hyper‐Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes," Risk Analysis, John Wiley & Sons, vol. 35(5), pages 919-930, May.
    3. Xun-Jian Li & Guo-Liang Tian & Mingqian Zhang & George To Sum Ho & Shuang Li, 2023. "Modeling Under-Dispersed Count Data by the Generalized Poisson Distribution via Two New MM Algorithms," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    4. Royce A. Francis & Srinivas Reddy Geedipally & Seth D. Guikema & Soma Sekhar Dhavala & Dominique Lord & Sarah LaRocca, 2012. "Characterizing the Performance of the Conway‐Maxwell Poisson Generalized Linear Model," Risk Analysis, John Wiley & Sons, vol. 32(1), pages 167-183, January.
    5. Jinxian Weng & Qiang Meng & David Z. W. Wang, 2013. "Tree‐Based Logistic Regression Approach for Work Zone Casualty Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 33(3), pages 493-504, March.
    6. Muhammed Rasheed Irshad & Sreedeviamma Aswathy & Radhakumari Maya & Saralees Nadarajah, 2023. "New One-Parameter Over-Dispersed Discrete Distribution and Its Application to the Nonnegative Integer-Valued Autoregressive Model of Order One," Mathematics, MDPI, vol. 12(1), pages 1-14, December.
    7. Aghabazaz, Zeynab & Kazemi, Iraj, 2023. "Under-reported time-varying MINAR(1) process for modeling multivariate count series," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    8. Zhou, Can & Jiao, Yan & Browder, Joan, 2019. "K-aggregated transformation of discrete distributions improves modeling count data with excess ones," Ecological Modelling, Elsevier, vol. 407(C), pages 1-1.
    9. Shital A. Thekdi & James H. Lambert, 2012. "Decision Analysis and Risk Models for Land Development Affecting Infrastructure Systems," Risk Analysis, John Wiley & Sons, vol. 32(7), pages 1253-1269, July.
    10. Hwachyi Wang & S. K. Jason Chang & Hans De Backer & Dirk Lauwers & Philippe De Maeyer, 2019. "Integrating Spatial and Temporal Approaches for Explaining Bicycle Crashes in High-Risk Areas in Antwerp (Belgium)," Sustainability, MDPI, vol. 11(13), pages 1-28, July.
    11. Özkan Uğurlu & Serdar Yıldız & Sean Loughney & Jin Wang & Shota Kuntchulia & Irakli Sharabidze, 2020. "Analyzing Collision, Grounding, and Sinking Accidents Occurring in the Black Sea Utilizing HFACS and Bayesian Networks," Risk Analysis, John Wiley & Sons, vol. 40(12), pages 2610-2638, December.
    12. Bermúdez, Lluís & Guillén, Montserrat & Karlis, Dimitris, 2018. "Allowing for time and cross dependence assumptions between claim counts in ratemaking models," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 161-169.
    13. Luiza S. C. Piancastelli & Wagner Barreto‐Souza & Hernando Ombao, 2023. "Flexible bivariate INGARCH process with a broad range of contemporaneous correlation," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 206-222, March.
    14. Katiane S. Conceição & Marinho G. Andrade & Victor Hugo Lachos & Nalini Ravishanker, 2024. "Bayesian Inference for Zero-Modified Power Series Regression Models," Mathematics, MDPI, vol. 13(1), pages 1-30, December.
    15. Kai Yang & Yiwei Zhao & Han Li & Dehui Wang, 2023. "On bivariate threshold Poisson integer-valued autoregressive processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 931-963, November.
    16. Dongying Zhan & Derek S. Young, 2024. "Finite mixtures of mean-parameterized Conway–Maxwell–Poisson models," Statistical Papers, Springer, vol. 65(3), pages 1469-1492, May.
    17. Boris Forthmann & Philipp Doebler, 2021. "Reliability of researcher capacity estimates and count data dispersion: a comparison of Poisson, negative binomial, and Conway-Maxwell-Poisson models," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(4), pages 3337-3354, April.
    18. Dominique Lord & Srinivas Reddy Geedipally & Seth D. Guikema, 2010. "Extension of the Application of Conway‐Maxwell‐Poisson Models: Analyzing Traffic Crash Data Exhibiting Underdispersion," Risk Analysis, John Wiley & Sons, vol. 30(8), pages 1268-1276, August.
    19. N. Mamode Khan & Y. Sunecher & V. Jowaheer & M. M. Ristic & M. Heenaye-Mamode Khan, 2019. "Investigating GQL-based inferential approaches for non-stationary BINAR(1) model under different quantum of over-dispersion with application," Computational Statistics, Springer, vol. 34(3), pages 1275-1313, September.
    20. 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).

    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:gam:jstats:v:8:y:2025:i:1:p:22-:d:1610824. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.