We propose a generalized non‐linear state‐space model for count‐valued time series of COVID‐19 fatalities. To capture the dynamic changes in daily COVID‐19 death counts, we specify a latent state process that involves second‐order differencing and an AR(1)‐ARCH(1) model. These modelling choices are motivated by the application and validated by model assessment. We consider and fit a progression of Bayesian hierarchical models under this general framework. Using COVID‐19 daily death counts from New York City's five boroughs, we evaluate and compare the considered models through predictive model assessment. Our findings justify the elements included in the proposed model. The proposed model is further applied to time series of COVID‐19 deaths from the four most populous counties in Texas. These model fits illuminate dynamics associated with multiple dynamic phases and show the applicability of the framework to localities beyond New York City.

中文翻译：

---

COVID-19 每日死亡动态的计数值时间序列模型


我们提出了一种适用于 COVID-19 死亡人数计数值时间序列的广义非线性状态空间模型。为了捕获每日 COVID-19 死亡人数的动态变化，我们指定了一个涉及二阶差分和 AR(1)-ARCH(1) 模型的潜在状态过程。这些建模选择是由应用程序驱动的，并通过模型评估进行验证。我们在这个总体框架下考虑并拟合一系列贝叶斯分层模型。我们使用纽约市五个行政区的 COVID-19 每日死亡人数，通过预测模型评估来评估和比较所考虑的模型。我们的研究结果证明了拟议模型中包含的要素的合理性。所提出的模型进一步应用于德克萨斯州人口最多的四个县的 COVID-19 死亡时间序列。这些模型拟合阐明了与多个动态阶段相关的动态，并显示了该框架对纽约市以外地区的适用性。