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 drift component, a Brownian component and finite variation jumps, they show that it is possible to identify when the cause is a drift burst (the statistic explodes) or otherwise (the statistic is asymptotically Gaussian). We complete the investigation showing how infinite variation jumps contribute asymptotically.
The result is that the jumps never cause the explosion of the statistic. Specifically, when there are no bursts, the statistic diverges only if the Brownian component is absent, the jumps have finite variation and the drift is non-zero. In this case the triggering is precisely the drift.
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
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