Mixing Properties Of Integer-Valued Garch Processes

We consider models for count variables with a GARCH-type structure. Such a process consists of an integer-valued component and a volatility process. Using arguments for contractive Markov chains we prove that this bivariate process has a unique stationary regime. Furthermore, we show absolute regularity (beta-mixing) with geometrically decaying coefficients for the count process. These probabilistic results are complemented by a statistical analysis and a few simulations.