Efficient estimation in periodic [formula omitted] model: Nonparametric innovation distributions case

Abstract

The efficient estimation problem of a semi-parametric periodic integer-valued autoregressive PINARp model of arbitrary order is considered. The unspecified distribution of the innovation process of this model is supposed to satisfy only some mild technical assumptions.We therefore provide efficient estimates for both parameters of the model, namely a periodic autoregressive parameter and a periodic probability law of the innovation non-negative integer values process which is seen as an infinite dimensional parameter. The performances of these efficient estimations are shown through an intensive simulation study and an application on real data set.