Testing whether jumps have finite or infinite activity
  We propose statistical tests to discriminate between the finite and infinite activity of jumps in a semimartingale discretely observed at high frequency. The two statistics allow for a symmetric treatment of the problem: we can either take the null hypothesis to be finite activity, or infinite activity. When implemented on high-frequency stock returns, both tests point toward the presence of infinite-activity jumps in the data. 
Yacine A\"it-Sahalia, Jean Jacod
math.ST stat.TH