Mixing properties of non‐stationary multi‐variate count processes

We consider multi‐variate versions of two popular classes of integer‐valued processes. While the transition mechanism is time‐homogeneous, a possible non‐stationarity is introduced by an exogeneous covariate process. We prove absolute regularity (‐mixing) for the count process with exponentially decaying mixing coefficients. The proof of this result makes use of some sort of contraction in the transition mechanism which allows a coupling of two versions of the count process such that they eventually coalesce. We show how this result can be used to prove asymptotic normality of a least squares estimator of an involved model parameter.