Conditional-mean Multiplicative Operator Models for Count Time Series

TL;DR

This paper introduces a new class of count time series models called CMEMs, which extend multiplicative error models to discrete data using a novel multiplicative operator, and explores their properties and applications.

Contribution

It proposes a new multiplicative operator for count data, developing CMEMs that relate to INGARCH models and extend their semi-parametric capabilities.

Findings

CMEMs can be estimated using quasi-maximum likelihood and weighted least squares.

Simulation studies demonstrate the effectiveness of CMEMs.

Real-world data examples validate the applicability of the proposed models.

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.