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.

CEMAT - Center for Computational and Stochastic Mathematics