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

Author

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  • 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
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    References listed on IDEAS

    as
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    2. Saralees Nadarajah, 2009. "Useful moment and CDF formulations for the COM–Poisson distribution," Statistical Papers, Springer, vol. 50(3), pages 617-622, June.
    3. 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.
    4. 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.
    5. 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.
    6. Pedeli, Xanthi & Karlis, Dimitris, 2013. "Some properties of multivariate INAR(1) processes," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 213-225.
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