IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v34y2019i3d10.1007_s00180-018-0836-5.html
   My bibliography  Save this article

Investigating GQL-based inferential approaches for non-stationary BINAR(1) model under different quantum of over-dispersion with application

Author

Listed:
  • N. Mamode Khan

    (University of Mauritius)

  • Y. Sunecher

    (University of Technology Mauritius)

  • V. Jowaheer

    (University of Mauritius)

  • M. M. Ristic

    (University of Nis)

  • M. Heenaye-Mamode Khan

    (University of Mauritius)

Abstract

In particular, this paper addresses solutions to the computational challenges encountered in estimating parameters in non-stationary over-dispersed bivariate integer-valued autoregressive of order 1 (BINAR(1)) model with Negative Binomial (NB) innovations. In this BINAR(1) model, the cross-correlation is induced through the paired NB innovations which follows a recently introduced bivariate NB model under different over-dispersion indices. The estimation of the model parameters is conducted via a two-phased generalized quasi-likelihood (GQL) approach but the second GQLs auto-covariance structure constitutes of higher-order moment entries which are not readily available in closed form. In this context, two GQL approaches: GQL $$_{MVN}$$ MVN based on approximating the higher-order covariances through the multivariate normality structure and GQL $$_{BT}$$ BT based on deriving the exact higher-order covariances by some novel high-dimensional thinning properties are proposed and compared. The asymptotic properties of the respective GQLs are derived. Monte-Carlo simulation experiments are implemented to investigate on the performance of the GQLs, the consistency and the asymptotic efficiency of the estimates. The proposed model and the estimation methodologies are applied to a real-life time series data in the Transport sector in Mauritius. The root mean square error based on some out-sample statistics are also computed to assess the reliability of the model.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:compst:v:34:y:2019:i:3:d:10.1007_s00180-018-0836-5
    DOI: 10.1007/s00180-018-0836-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-018-0836-5
    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/s00180-018-0836-5?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. Predrag M. Popović & Miroslav M. Ristić & Aleksandar S. Nastić, 2016. "A geometric bivariate time series with different marginal parameters," Statistical Papers, Springer, vol. 57(3), pages 731-753, September.
    2. Brajendra C. Sutradhar, 2008. "On forecasting counts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(2), pages 109-129.
    3. Pedeli, Xanthi & Karlis, Dimitris, 2013. "Some properties of multivariate INAR(1) processes," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 213-225.
    4. Vandna Jowaheer, 2002. "Analysing longitudinal count data with overdispersion," Biometrika, Biometrika Trust, vol. 89(2), pages 389-399, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cláudia Santos & Isabel Pereira & Manuel G. Scotto, 2021. "On the theory of periodic multivariate INAR processes," Statistical Papers, Springer, vol. 62(3), pages 1291-1348, June.

    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. Yuvraj Sunecher & Naushad Mamode Khan & Miroslav M. Ristić & Vandna Jowaheer, 2019. "BINAR(1) negative binomial model for bivariate non-stationary time series with different over-dispersion indices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 625-653, December.
    2. Qingchun Zhang & Dehui Wang & Xiaodong Fan, 2020. "A negative binomial thinning‐based bivariate INAR(1) process," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 517-537, November.
    3. 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.
    4. Christoph Jeßberger, 2011. "Multilateral Environmental Agreements up to 2050: Are They Sustainable Enough?," ifo Working Paper Series 98, ifo Institute - Leibniz Institute for Economic Research at the University of Munich.
    5. Predrag M. Popović & Hassan S. Bakouch, 2020. "A bivariate integer-valued bilinear autoregressive model with random coefficients," Statistical Papers, Springer, vol. 61(5), pages 1819-1840, October.
    6. Alwell J. Oyet & Brajendra C. Sutradhar, 2021. "Analyzing Unevenly Spaced Longitudinal Count Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 342-373, November.
    7. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    8. 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).
    9. Brajendra C. Sutradhar & Vandna Jowaheer & R. Prabhakar Rao, 2016. "Semi-Parametric Models for Negative Binomial Panel Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 269-303, August.
    10. Jowaheer, Vandna, 2006. "Model misspecification effects in clustered count data analysis," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 470-478, March.
    11. Darolles, Serge & Fol, Gaëlle Le & Lu, Yang & Sun, Ran, 2019. "Bivariate integer-autoregressive process with an application to mutual fund flows," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 181-203.
    12. Simon Nik & Christian H. Weiß, 2020. "CLAR(1) point forecasting under estimation uncertainty," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 489-516, November.
    13. 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.
    14. 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.
    15. Miroslav M. Ristić & Yuvraj Sunecher & Naushad Mamode Khan & Vandna Jowaheer, 2019. "A GQL-based inference in non-stationary BINMA(1) time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 969-998, September.
    16. Brajendra C. Sutradhar, 2008. "On forecasting counts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(2), pages 109-129.
    17. Dimitris Karlis & Naushad Mamode Khan & Yuvraj Sunecher, 2024. "The Negative Binomial INAR(1) Process under Different Thinning Processes: Can We Separate between the Different Models?," Stats, MDPI, vol. 7(3), pages 1-15, July.
    18. Fokianos, Konstantinos, 2024. "Multivariate Count Time Series Modelling," Econometrics and Statistics, Elsevier, vol. 31(C), pages 100-116.
    19. Yuvraj Sunecher & Naushad Mamode Khan, 2024. "On Comparing and Assessing Robustness of Some Popular Non-Stationary BINAR(1) Models," JRFM, MDPI, vol. 17(3), pages 1-13, February.
    20. Ye, Fei & Yue, Chen & Yang, Ying, 2013. "Modeling time-dependent overdispersion in longitudinal count data," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 257-264.

    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:compst:v:34:y:2019:i:3:d:10.1007_s00180-018-0836-5. 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.