The max-BARMA models for counts with bounded support

In this note, we introduce a discrete counterpart of the conventional max-autoregressive moving-average process of Davis and Resnick (1989), based on the binomial thinning operator and driven by a sequence of i.  i.  d. nonnegative integer-valued random variables with a finite range of counts. Basic probabilistic and statistical properties of this new class of models are discussed in detail, namely the existence of a stationary distribution, and how observations' and innovations' distributions are related to each other. Furthermore, parameter estimation is also addressed.