Unified inference for an integer-valued AR(1) model

Conditional least squares estimation is often employed to infer an integer-valued AR(1) model and its convergence rate and asymptotic variance differ for the stable and nearly unstable cases. This article adopts a random weighted bootstrap method to provide a unified interval estimation and hypothesis test regardless of the underlying process being either stable or nearly unstable. A simulation study confirms the good finite sample performance of the proposed inference. We also apply it to test for a unit root test in a COVID-19 dataset.