We consider the test statistic devised by Christensen, Oomen and Renò in 2020 to obtain insight into the causes of flash crashes occurring at particular moments in time in the price of a financial asset. Under an Ito semimartingale model containing a Brownian component and finite variation jumps, it is possible to distinguish when the cause is a drift burst (the statistic explodes) or not (it is asymptotically Gaussian). We complete the investigation showing how infinite variation jumps contribute asymptotically.
The result is that, when there are no bursts, explosion only can occur in the absence of the Brownian part and when the jumps have finite variation. In that case the explosion is due to the compensator of the small jumps.
We also find that the statistic could be adopted for a variety of tests useful for investigating the nature of the data generating process, given discrete observations.