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arXiv · 2212.05831

Conditional-mean Multiplicative Operator Models for Count Time Series

Christian H. Weiß·Fukang Zhu
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Abstract

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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BibTeXRIS

Christian H. Weiß, Fukang Zhu. 2023-11-27. Conditional-mean Multiplicative Operator Models for Count Time Series. https://doi.org/10.1016/j.csda.2023.107885

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