The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but a generalized network (termed a graph with Euclidean edges). Additionally, data are repeatedly measured over different temporal instants. We provide new classes of nonseparable space-time stationary covariance functions where {\em space} can be a generalized network, a Euclidean tree, or a linear network, and where time can be linear or circular (seasonal). Because the construction principles are technical, we focus on illustrations that guide the reader through the construction of statistically interpretable examples. A simulation study demonstrates that we can recover the correct model when compared to misspecified models. In addition, our simulation studies show that we effectively recover simulation parameters. In our data analysis, we consider a traffic accident dataset that shows improved model performance based on covariance specifications and network-based metrics.

中文翻译：

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跨时间网络上的不可分时空平稳协方差函数

数据科学的出现带来了越来越多的高数据复杂性挑战。本文解决了时空数据的挑战，其中空间域不是平面、球体或线性网络，而是广义网络（称为具有欧几里得边的图）。此外，在不同的时间瞬间重复测量数据。我们提供了新类别的不可分时空平稳协方差函数，其中 {\em space} 可以是广义网络、欧几里得树或线性网络，其中时间可以是线性或循环（季节性）。因为构建原则是技术性的，所以我们专注于通过构建统计上可解释的示例来指导读者的插图。模拟研究表明，与错误指定的模型相比，我们可以恢复正确的模型。此外，我们的模拟研究表明，我们有效地恢复了模拟参数。在我们的数据分析中，我们考虑了一个交通事故数据集，该数据集显示了基于协方差规范和基于网络的指标的改进模型性能。