New tests for jumps: a threshold-based approach

In this paper we propose a test to determine whether jumps are present in a discretely sampled process or not. We use the concept of truncated power variation to construct our test statistics for (i) semimartingale models and (ii) semimartingale models with noise. The test statistics converge to infinity if jumps are present and have a normal distribution otherwise. Our method is valid (under very weak assumptions) for all semimartingales with absolute continuous characteristics and rather general model for the noise process. We finally implement the test and present the simulation results. Our simulations suggest that for semimartingale models the new test is much more powerful then tests proposed by Barndorff-Nielsen and Shephard (2006) and Aït-Sahalia and Jacod (2008).