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 &sqrt;h, was obtained when the jump components have finite activity. Here we show that the speed is &sqrt;h only when the activity of the jump components is moderate.
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