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

Huiqiao Wang (), Christian H. Weiß () and Mingming Zhang ()
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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

AStA Advances in Statistical Analysis, 2025, vol. 109, issue 2, No 2, 279 pages

Abstract: 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.

Keywords: Asymptotic distribution; Bivariate dispersion index; Bivariate INAR(1) model; Bivariate Poisson distribution; Count time series (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10182-024-00512-3

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