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We investigate whether spatial-kinematic substructure in young star-formingregions can be quantified using Moran's $I$ statistic. Its presence in youngstar clusters would provide an indication that the system formed from initiallysubstructured conditions, as expected by the hierarchical model of star clusterformation, even if the cluster were spatially smooth and centrallyconcentrated. Its absence, on the other hand, would be evidence that starclusters form monolithically. The Moran's $I$ statistic is applied to $N$-bodysimulations of star clusters with different primordial spatial-velocitystructures, and its evolution over time is studied. It is found that thisstatistic can be used to reliably quantify spatial-kinematic substructure, andcan be used to provide evidence as to whether the spatial-kinematic structureof regions with ages $\lesssim$ 6 Myr is best reproduced by the hierarchical ormonolithic models of star formation. Moran's $I$ statistic is also able toconclusively say whether the data are $not$ consistent with initial conditionsthat lack kinematic substructure, such as the monolithic model, in regions withages up to, and potentially beyond, 10 Myrs. This can therefore provide akinematic signature of the star cluster formation process that is observablefor many Myr after any initial spatial structure has been erased.

Quantifying kinematic substructure in star-forming regions with statistical tests of spatial autocorrelation