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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
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