  We consider a stochastic process driven by a diffusion and jumps. We devise a
technique, which is based on a discrete record of observations, for identifying
the times when jumps larger than a suitably defined threshold occurred. The
technique allows also jump size estimation. We prove the consistency of a
nonparametric estimator of the integrated infinitesimal variance of the process
continuous part when the jump component with infinite activity is Levy. Central
limit results are proved in the case where the jump component has finite
activity. Some simulations illustrate the reliability of the methodology in
finite samples.
