  Time series of counts are frequently analyzed using generalized
integer-valued autoregressive models with conditional heteroskedasticity
(INGARCH). These models employ response functions to map a vector of past
observations and past conditional expectations to the conditional expectation
of the present observation. In this paper, it is shown how INGARCH models can
be combined with artificial neural network (ANN) response functions to obtain a
class of nonlinear INGARCH models. The ANN framework allows for the
interpretation of many existing INGARCH models as a degenerate version of a
corresponding neural model. Details on maximum likelihood estimation, marginal
effects and confidence intervals are given. The empirical analysis of time
series of bounded and unbounded counts reveals that the neural INGARCH models
are able to outperform reasonable degenerate competitor models in terms of the
information loss.
