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.
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