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The efficient estimation problem of a semi-parametric first-order periodic integer-valued autoregressive ( PINAR (1)) model is considered. The unspecified distribution of the innovation process of this model is suposed 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 intensive simulations studies and an application on real data set.

Efficient estimation in ( PINAR (1)) model: semiparametric case