  Given a stationary point process, an intensity burst is defined as a short
time period during which the number of counts is larger than the typical count
rate. It might signal a local non-stationarity or the presence of an external
perturbation to the system. In this paper we propose a novel procedure for the
detection of intensity bursts within the Hawkes process framework. By using a
model selection scheme we show that our procedure can be used to detect
intensity bursts when both their occurrence time and their total number is
unknown. Moreover, the initial time of the burst can be determined with a
precision given by the typical inter-event time. We apply our methodology to
the mid-price change in FX markets showing that these bursts are frequent and
that only a relatively small fraction is associated to news arrival. We show
lead-lag relations in intensity burst occurrence across different FX rates and
we discuss their relation with price jumps.
