  Multivariate Hawkes processes (MHP) are a class of point processes in which
events at different coordinates interact through mutual excitation. The
weighted adjacency matrix of the MHP encodes the strength of the relations, and
shares its support with the causal graph of interactions of the process. We
consider the problem of testing for causal relationships across the dimensions
of a marked MHP. The null hypothesis is that a joint group of adjacency
coefficients are null, corresponding to the absence of interactions. The
alternative is that they are positive, and the associated interactions do
exist. To this end, we introduce a novel estimation procedure in the context of
a large sample of independent event sequences. We construct the associated
likelihood ratio test and derive the asymptotic distribution of the test
statistic as a mixture of chi squared laws. We offer two applications on
financial datasets to illustrate the performance of our method. In the first
one, our test reveals a deviation from a static equilibrium in bidders'
strategies on retail online auctions. In the second one, we uncover some
factors at play in the dynamics of German intraday power prices.
