In this paper we introduce a multiplicative integer-valued time series model, which is defined as the product of a unit-mean integer-valued independent and identically distributed (iid) sequence, and an integer-valued dependent process. The latter is defined as a binomial thinning operation of its own past and of the past of the observed process. Furthermore, it combines some features of the integer-valued GARCH (INGARCH), the autoregressive conditional duration (ACD), and the integer autoregression (INAR) processes. The proposed model has an unspecified distribution and is able to parsimoniously generate very high overdispersion, persistence, and heavy-tailedness. The dynamic probabilistic structure of the model is first analyzed. In addition, parameter estimation is considered by using a two-stage weighted least squares estimate (2SWLSE), consistency and asymptotic normality (CAN) of which are established under mild conditions. Applications of the proposed formulation to simulated and actual count time series data are provided.

CEMAT - Center for Computational and Stochastic Mathematics