Locally asymptotically efficient estimation for parametric PINAR(p) models

This article focuses on the efficient estimation problem of an arbitrary‐order periodic integer‐valued autoregressive (PINAR(p)) model. Both the local asymptotic normality (LAN) property and the local asymptotic linearity property satisfied by the central sequence of the underlying model are established. Using these results, we construct efficient estimators for the parameters in a parametric framework. The consistency property of these efficient estimations is evaluated via an intensive simulation study. Moreover, the performances of these efficient estimations, over the conditional maximum likelihood (CML) and the conditional least squares (CLS) estimations, are also illustrated via an intensive simulation study and an application on real data set.