  Many fits of Hawkes processes to financial data look rather good but most of
them are not statistically significant. This raises the question of what part
of market dynamics this model is able to account for exactly. We document the
accuracy of such processes as one varies the time interval of calibration and
compare the performance of various types of kernels made up of sums of
exponentials. Because of their around-the-clock opening times, FX markets are
ideally suited to our aim as they allow us to avoid the complications of the
long daily overnight closures of equity markets. One can achieve statistical
significance according to three simultaneous tests provided that one uses
kernels with two exponentials for fitting an hour at a time, and two or three
exponentials for full days, while longer periods could not be fitted within
statistical satisfaction because of the non-stationarity of the endogenous
process. Fitted timescales are relatively short and endogeneity factor is high
but sub-critical at about 0.8.
