  Integer-valued time series exist widely in economics, finance, biology,
computer science, medicine, insurance, and many other fields. In recent years,
many types of models have been proposed to model integer-valued time series
data, in which the integer autoregressive model and integer-valued GARCH model
are the most representative. Although there have been many results of
integer-valued time series data, the parameters of integer-valued time series
model structure are more complicated. This paper is dedicated to proposing a
new simple integer-valued GARCH model. First, the Bell integer-valued GARCH
model is given based on Bell distribution. Then, the conditional maximum
likelihood estimation method is used to obtain the estimators of parameters.
Later, numerical simulations confirm the finite sample properties of the
estimation of unknown parameters. Finally, the model is applied in the two real
examples. Compared with the existing models, the proposed model is more simple
and applicable.
