  Multiplicative error models (MEMs) are commonly used for real-valued time
series, but they cannot be applied to discrete-valued count time series as the
involved multiplication would not preserve the integer nature of the data.
Thus, the concept of a multiplicative operator for counts is proposed (as well
as several specific instances thereof), which are then used to develop a kind
of MEMs for count time series (CMEMs). If equipped with a linear conditional
mean, the resulting CMEMs are closely related to the class of so-called
integer-valued generalized autoregressive conditional heteroscedasticity
(INGARCH) models and might be used as a semi-parametric extension thereof.
Important stochastic properties of different types of INGARCH-CMEM as well as
relevant estimation approaches are derived, namely types of quasi-maximum
likelihood and weighted least squares estimation. The performance and
application are demonstrated with simulations as well as with two real-world
data examples.
