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

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.