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Specifications tests for count time series models with covariates

Author

Listed:
  • Šárka Hudecová

    (Charles University)

  • Marie Hušková

    (Charles University)

  • Simos G. Meintanis

    (National and Kapodistrian University of Athens
    North–West University)

Abstract

We propose a goodness-of-fit test for a class of count time series models with covariates which includes the Poisson autoregressive model with covariates (PARX) as a special case. The test criteria are derived from a specific characterization for the conditional probability generating function, and the test statistic is formulated as a $$L_2$$ L 2 weighting norm of the corresponding sample counterpart. The asymptotic properties of the proposed test statistic are provided under the null hypothesis as well as under specific alternatives. A bootstrap version of the test is explored in a Monte–Carlo study and illustrated on a real data set on road safety.

Suggested Citation

  • Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2024. "Specifications tests for count time series models with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(4), pages 1014-1040, December.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:4:d:10.1007_s11749-024-00933-x
    DOI: 10.1007/s11749-024-00933-x
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