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

Nonseparable Space-Time Stationary Covariance Functions on Networks cross Time