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A Semiparametric Approach to Test for the Presence of INAR: Simulations and Empirical Applications

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  • Lucio Palazzo

    (Department of Political Sciences, University of Naples Federico II, 80138 Naples, Italy)

  • Riccardo Ievoli

    (Department of Chemical, Pharmaceutical and Agricultural Sciences, University of Ferrara, 44121 Ferrara, Italy)

Abstract

The present paper explores the application of bootstrap methods in testing for serial dependence in observed driven Integer-AutoRegressive (models) considering Poisson arrivals (P-INAR). To this end, a new semiparametric and restricted bootstrap algorithm is developed to ameliorate the performance of the score-based test statistic, especially when the time series present small or moderately small lengths. The performance of the proposed bootstrap test, in terms of empirical size and power, is investigated through a simulation study even considering deviation from Poisson assumptions for innovations, i.e., overdispersion and underdispersion. Under non-Poisson innovations, the semiparametric bootstrap seems to “restore” inference, while the asymptotic test usually fails. Finally, the usefulness of this approach is shown via three empirical applications.

Suggested Citation

  • Lucio Palazzo & Riccardo Ievoli, 2022. "A Semiparametric Approach to Test for the Presence of INAR: Simulations and Empirical Applications," Mathematics, MDPI, vol. 10(14), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2501-:d:865526
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    References listed on IDEAS

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