A New Integer-Valued AR(1) Process Based on Power Series Thinning Operator

In this paper, we introduce the first-order non-negative integer-valued autoregressive (INAR(1)) process with Poisson-Lindley innovations based on a new thinning operator called power series thinning operator. Some statistical properties of process are given. The unknown parameters of the model are estimated by three methods; the conditional least squares, Yule-Walker and conditional maximum likelihood. Then, the performances of these estimators are evaluated using simulation study. Three special cases of model are investigated in some detail. Finally, the model is applied to four real data sets, such as the annual number of earthquakes, the monthly number of measles cases, the numbers of sudden death series and weekly counts of the incidence of acute febrile muco-cutaneous lymph node syndrome. Then we show the potentiality of the model.