A New INAR(1) Model for ℤ-Valued Time Series Using the Relative Binomial Thinning Operator

Abstract

Abstract A new first-order integer-valued autoregressive process (INAR(1)) with extended Poisson innovations is introduced based on a signed version of the thinning operator, called relative binomial thinning operator, which can be considered as an extension of standard binomial thinning operator introduced by Steutel, F.W. and van Harn, K. (1979. Discrete analogues of self-decomposability and stability. Ann. Probab. 7: 893–899). It is appropriate for modeling Z $\mathbb{Z}$ -valued time series and either positive or negative correlations. Some properties of the process are established. Conditional least squares, Yule–Walker and conditional maximum likelihood methods are considered for the parameter estimation of the model. Moreover, simulation experiments are carried out to attest to the performance of the estimation methods. The applicability of the proposed model is investigated through a practical data set of the Saudi stock market.