  In this paper we consider two processes driven by diffusions and jumps. The
jump components are Levy processes and they can both have finite activity and
infinite activity. Given discrete observations we estimate the covariation
between the two diffusion parts and the co-jumps. The detection of the co-jumps
allows to gain insight in the dependence structure of the jump components and
has important applications in finance. Our estimators are based on a threshold
principle allowing to isolate the jumps. This work follows Gobbi and Mancini
(2006) where the asymptotic normality for the estimator of the covariation,
with convergence speed given by the squared root of h, was obtained when the
jump components have finite activity. Here we show that the speed is the
squared root of h only when the activity of the jump components is moderate.
