A PRACTICAL INFERENCE FOR DISCRETELY OBSERVED JUMP-DIFFUSIONS FROM FINITE SAMPLES

In the inference for jump-diffusion processes, we often need to get the information of the jump part and of the continuous part separately from the data. Although some asymptotic theories have been studied on this issue, a practical interest is the inference from finitely many discrete samples. In this paper we propose a numerical procedure to construct a filter to judge whether or not a jump occurred from finite samples. The paper includes a discussion about the validity of the procedure.