  The asymptotic distribution of the score test of the null hypothesis that
marks do not impact the intensity of a Hawkes marked self-exciting point
process is shown to be chi-squared. For local asymptotic power, the
distribution against local alternatives is also established as non-central
chi-squared. These asymptotic results are derived using existing asymptotic
results for likelihood estimates of the unmarked Hawkes process model together
with mild additional conditions on the moments and ergodicity of the marks
process and an additional uniform boundedness assumption, shown to be true for
the exponential decay Hawkes process.
