  In this paper, we introduce the first-order integer-valued autoregressive
(INAR(1)) model, with Poisson-Lindley innovations based on power series
thinning operator. Some mathematical features of this process are given and
estimating the parameters is discussed by three methods; conditional least
squares, Yule-Walker equations and conditional maximum likelihood.Then the
results are studied for three special cases of power series operators. Finally,
some numerical results are presented with a discussion to the obtained results
and Four real data sets are used to show the potentially of the new process.
