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Conditional-mean Multiplicative Operator Models for Count Time Series. (arXiv:2212.05831v2 [stat.ME] UPDATED)

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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.

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