  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.
