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Testing the compounding structure of the CP-INARCH model

Author

Listed:
  • Christian H. Weiß

    (Helmut Schmidt University)

  • Esmeralda Gonçalves

    (Universidade de Coimbra)

  • Nazaré Mendes Lopes

    (Universidade de Coimbra)

Abstract

A statistical test to distinguish between a Poisson INARCH model and a Compound Poisson INARCH model is proposed, based on the form of the probability generating function of the compounding distribution of the conditional law of the model. For first-order autoregression, the normality of the test statistics’ asymptotic distribution is established, either in the case where the model parameters are specified, or when such parameters are consistently estimated. As the test statistics’ law involves the moments of inverse conditional means of the Compound Poisson INARCH process, the analysis of their existence and calculation is performed by two approaches. For higher-order autoregressions, we use a bootstrap implementation of the test. A simulation study illustrating the finite-sample performance of this test methodology in what concerns its size and power concludes the paper.

Suggested Citation

  • Christian H. Weiß & Esmeralda Gonçalves & Nazaré Mendes Lopes, 2017. "Testing the compounding structure of the CP-INARCH model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(5), pages 571-603, July.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:5:d:10.1007_s00184-017-0617-0
    DOI: 10.1007/s00184-017-0617-0
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    References listed on IDEAS

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    Cited by:

    1. Weiß, Christian H. & Zhu, Fukang, 2024. "Conditional-mean multiplicative operator models for count time series," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    2. 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.

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