  A common approach to analyze count time series is to fit models based on
random sum operators. As an alternative, this paper introduces time series
models based on a random multiplication operator, which is simply the
multiplication of a variable operand by an integer-valued random coefficient,
whose mean is the constant operand. Such operation is endowed into
auto-regressive-like models with integer-valued random inputs, addressed as
RMINAR. Two special variants are studied, namely the N0-valued random
coefficient auto-regressive model and the N0-valued random coefficient
multiplicative error model. Furthermore, Z-valued extensions are considered.
The dynamic structure of the proposed models is studied in detail. In
particular, their corresponding solutions are everywhere strictly stationary
and ergodic, a fact that is not common neither in the literature on
integer-valued time series models nor real-valued random coefficient
auto-regressive models. Therefore, the parameters of the RMINAR model are
estimated using a four-stage weighted least squares estimator, with consistency
and asymptotic normality established everywhere in the parameter space.
Finally, the new RMINAR models are illustrated with some simulated and
empirical examples.
