AZ-whiteness test: a test for uncorrelated noise on spatio-temporal graphs
This provides a tool for analyzing uncorrelated noise in spatio-temporal graph data, applicable to domains like transportation networks and sensor grids, but it is incremental as an extension of existing tests.
The authors introduced the first whiteness test for graphs, designed to detect serial and spatial dependencies in multivariate time series on dynamic graphs, and validated it on synthetic and real-world problems to assess spatio-temporal forecasting models.
We present the first whiteness test for graphs, i.e., a whiteness test for multivariate time series associated with the nodes of a dynamic graph. The statistical test aims at finding serial dependencies among close-in-time observations, as well as spatial dependencies among neighboring observations given the underlying graph. The proposed test is a spatio-temporal extension of traditional tests from the system identification literature and finds applications in similar, yet more general, application scenarios involving graph signals. The AZ-test is versatile, allowing the underlying graph to be dynamic, changing in topology and set of nodes, and weighted, thus accounting for connections of different strength, as is the case in many application scenarios like transportation networks and sensor grids. The asymptotic distribution -- as the number of graph edges or temporal observations increases -- is known, and does not assume identically distributed data. We validate the practical value of the test on both synthetic and real-world problems, and show how the test can be employed to assess the quality of spatio-temporal forecasting models by analyzing the prediction residuals appended to the graphs stream.