Econometrics of co-jumps in high-frequency data with noise

We establish estimation methods to determine co-jumps in multivariate high-frequency data with non-synchronous observations and market microstructure. A rate-optimal estimator of the entire quadratic covariation of an Itô-semimartingale is constructed by a locally adaptive spectral approach. Thresholding allows to disentangle the co-jump from the continuous part. We derive a feasible limit theorem for a truncated estimator of integrated covolatility which facilitates asymptotically efficient (co-)volatility estimation in the presence of jumps. A test for common jumps is presented. Simulations and an empirical application to intra-day tick-data from EUREX futures demonstrate the practical value of the approach.