The max-BARMA models for counts with bounded support
Weiss, Christian H.; Scotto, Manuel; Moller, Tobias A.; Gouveia, Sonia
Statistics and Probability Letters, 143 (2018), 28-36
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.