Department of Biostatistics and Data Science, Kansas University Medical Center, Kansas City, KS, United States of America.
Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, United States of America.
PLoS One. 2023 May 18;18(5):e0285769. doi: 10.1371/journal.pone.0285769. eCollection 2023.
A serially dependent Poisson process with time-varying zero-inflation is proposed. Such formulations have the potential to model count data time series arising from phenomena such as infectious diseases that ebb and flow over time. The model assumes that the intensity of the Poisson process evolves according to a generalized autoregressive conditional heteroscedastic (GARCH) formulation and allows the zero-inflation parameter to vary over time and be governed by a deterministic function or by an exogenous variable. Both the expectation maximization (EM) and the maximum likelihood estimation (MLE) approaches are presented as possible estimation methods. A simulation study shows that both parameter estimation methods provide good estimates. Applications to two real-life data sets on infant deaths due to influenza show that the proposed integer-valued GARCH (INGARCH) model provides a better fit in general than existing zero-inflated INGARCH models. We also extended a non-linear INGARCH model to include zero-inflation and an exogenous input. This extended model performed as well as our proposed model with respect to some criteria, but not with respect to all.
提出了一个具有时变零膨胀的序列相关泊松过程。这种公式有可能对传染病等随时间起伏的现象产生的计数数据时间序列进行建模。该模型假设泊松过程的强度根据广义自回归条件异方差（GARCH）公式演变，并允许零膨胀参数随时间变化，并由确定性函数或外生变量控制。提出了期望最大化（EM）和最大似然估计（MLE）方法作为可能的估计方法。一项模拟研究表明，这两种参数估计方法都提供了良好的估计值。对两个关于流感导致婴儿死亡的实际数据集的应用表明，与现有的零膨胀 INGARCH 模型相比，所提出的整数值 GARCH（INGARCH）模型通常具有更好的拟合度。我们还将一个非线性 INGARCH 模型扩展到包含零膨胀和外部输入。这个扩展模型在某些标准上的表现与我们提出的模型一样好，但并不是所有标准。
