Integer-valued autoregressive processes with pre-established marginals and innovations: a new perspective on count time series modeling

Abstract

Count time series is a recurring subject in the scientic literature due to its applicability to several real situations. The improvement of established methods and the development of new modeling techniques for these time series are necessary and important, not only for the theoretical evolution of this area of Statistics but also for a better representation of reality as amathematical-statisticalmodel. On this direction, the present work proposes an innovative methodology in the modeling of the integer auto regressive processes, jointly prespecifying in the same family the marginal distributions and innovations. The Double Geometric Integer Autoregressive process of rst-order is presented and characterized by several statistical properties. The inference is performed through conditional least squares, Yule-Walker, and maximum likelihood. In addition, the consistency and asymptotic normality of the estimators are veried. Computational simulation via Monte Carlo methods is used to verify the performance of the proposed estimators. Applications to real datasets are given proving the practical relevance of the model developed. Moreover, the comparison with competing models is presented in order to corroborate the competitiveness of the proposed model.