IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v109y2025i2d10.1007_s10182-024-00512-3.html
   My bibliography  Save this article

Goodness-of-fit testing in bivariate count time series based on a bivariate dispersion index

Author

Listed:
  • Huiqiao Wang

    (Biogas Institute of Ministry of Agriculture and Rural Affairs)

  • Christian H. Weiß

    (Helmut Schmidt University)

  • Mingming Zhang

    (Biogas Institute of Ministry of Agriculture and Rural Affairs)

Abstract

A common choice for the marginal distribution of a bivariate count time series is the bivariate Poisson distribution. In practice, however, when the count data exhibit zero inflation, overdispersion or non-stationarity features, such that a marginal bivariate Poisson distribution is not suitable. To test the discrepancy between the actual count data and the bivariate Poisson distribution, we propose a new goodness-of-fit test based on a bivariate dispersion index. The asymptotic distribution of the test statistic under the null hypothesis of a first-order bivariate integer-valued autoregressive model with marginal bivariate Poisson distribution is derived, and the finite-sample performance of the goodness-of-fit test is analyzed by simulations. A real-data example illustrate the application and usefulness of the test in practice.

Suggested Citation

  • Huiqiao Wang & Christian H. Weiß & Mingming Zhang, 2025. "Goodness-of-fit testing in bivariate count time series based on a bivariate dispersion index," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 109(2), pages 241-279, June.
    • Handle: RePEc:spr:alstar:v:109:y:2025:i:2:d:10.1007_s10182-024-00512-3
    DOI: 10.1007/s10182-024-00512-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-024-00512-3
    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/s10182-024-00512-3?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Schweer, Sebastian & Weiß, Christian H., 2014. "Compound Poisson INAR(1) processes: Stochastic properties and testing for overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 267-284.
    2. Youngmi Lee & Sangyeol Lee & Dag Tjøstheim, 2018. "Asymptotic normality and parameter change test for bivariate Poisson INGARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 52-69, March.
    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. Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2021. "Goodness–of–Fit Tests for Bivariate Time Series of Counts," Econometrics, MDPI, vol. 9(1), pages 1-20, March.
    2. Boris Aleksandrov & Christian H. Weiß, 2020. "Parameter estimation and diagnostic tests for INMA(1) processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 196-232, March.
    3. Wagner Barreto-Souza, 2019. "Mixed Poisson INAR(1) processes," Statistical Papers, Springer, vol. 60(6), pages 2119-2139, December.
    4. José M. R. Murteira & Mário A. G. Augusto, 2017. "Hurdle models of repayment behaviour in personal loan contracts," Empirical Economics, Springer, vol. 53(2), pages 641-667, September.
    5. Subhankar Chattopadhyay & Raju Maiti & Samarjit Das & Atanu Biswas, 2022. "Change‐point analysis through integer‐valued autoregressive process with application to some COVID‐19 data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 4-34, February.
    6. 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.
    7. Christian H. Weiß & Sebastian Schweer, 2015. "Detecting overdispersion in INARCH(1) processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 281-297, August.
    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. Mamadou Lamine Diop & William Kengne, 2023. "A general procedure for change-point detection in multivariate time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 1-33, March.
    10. 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.
    11. Simon Nik, 2024. "Marginal analysis of count time series in the presence of missing observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(4), pages 1105-1128, December.
    12. Layth C. Alwan & Christian H. Weiß, 2017. "INAR implementation of newsvendor model for serially dependent demand counts," International Journal of Production Research, Taylor & Francis Journals, vol. 55(4), pages 1085-1099, February.
    13. Yang, Kai & Yu, Xinyang & Zhang, Qingqing & Dong, Xiaogang, 2022. "On MCMC sampling in self-exciting integer-valued threshold time series models," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    14. Sebastian Schweer, 2016. "A Goodness-of-Fit Test for Integer-Valued Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 77-98, January.
    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. Boris Aleksandrov & Christian H. Weiß, 2020. "Testing the dispersion structure of count time series using Pearson residuals," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 325-361, September.
    17. Marcelo Bourguignon & Christian H. Weiß, 2017. "An INAR(1) process for modeling count time series with equidispersion, underdispersion and overdispersion," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 847-868, December.
    18. Raju Maiti & Atanu Biswas & Bibhas Chakraborty, 2018. "Modelling of low count heavy tailed time series data consisting large number of zeros and ones," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 407-435, August.
    19. Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2017. "Tests for Structural Changes in Time Series of Counts," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 843-865, December.
    20. R. Maya & Jie Huang & M. R. Irshad & Fukang Zhu, 2024. "On Poisson Moment Exponential Distribution with Associated Regression and INAR(1) Process," Annals of Data Science, Springer, vol. 11(5), pages 1741-1759, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:alstar:v:109:y:2025:i:2:d:10.1007_s10182-024-00512-3. 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.