The authors propose a simple model as an integer-valued analogue of the generalized autoregressive conditional heteroskedastic (GARCH(
)) model with Poisson deviates. Putting particular emphasis to the case
, it is shown, from a second-order point of view, that this integer-valued GARCH process is a standard ARMA(1,1) process. The problem of maximum likelihood estimation of the parameters is investigated and the asymptotic distribution of the estimators is derived. A numerical example and an application of this model to real time series are presented.