<Para ID="Par1">Integer-valued time series models have been a recurrent theme considered in many papers in the last three decades, but only a few of them have dealt with models on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$${\mathbb {Z}}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="double-struck">Z</mi> </math> </EquationSource> </InlineEquation> (that is, including both negative and positive integers). Our aim in this paper is to introduce a...</equationsource></equationsource></inlineequation></para>