A New Extension of Thinning-Based Random Coefficient Integer-Valued Autoregressive Models for Count Data

The aims of this paper is to deal with overdispersed integer time series. Thus, new thinning called Discete Lindley Distribution (DLD}) thinning was build. Based on the proposed thinning operator, a new Random Coefficient Integer-Valued Autoregressive (RCINAR) model is formulated and its statistical properties were established. Parameters estimation were carried out via the Yule-Walker, conditional least squares and conditional maximum likelihood methods. Properties of proposed estimators were studies through Monte Carlo simulation. Then, to compare the proposed process to existing models, a real data set is used. Finally, the model is used to fit weekly data of meningitis cases in Burkina Faso.