Identifying the diffusion covariation and the co-jumps given discrete observations

When the covariance between the risk factors of asset prices is due to both Brown- ian and jump components, the realized covariation (RC) approaches the sum of the integrated covariation (IC) with the sum of the co-jumps, as the observation fre- quency increases to infinity, in a finite and fixed time horizon. In this paper the two components are consistently separately estimated within a semimartingale frame- work with possibly infinite activity jumps. The threshold (or truncated) estimator ˆ ICn is used, which substantially excludes from RC all terms containing jumps. Un- like in Jacod (2007, Universite de Paris-6) and Jacod (2008, Stochastic Processes and Their Applications 118, 517–559), no assumptions on the volatilities’ dynamics are required. In the presence of only finite activity jumps: 1) central limit theorems (CLTs) for ˆ ICn and for further measures of dependence between the two Brownian parts are obtained; the estimation error asymptotic variance is shown to be smaller than for the alternative estimators of IC in the literature; 2) by also selecting the ob- servations as in Hayashi and Yoshida (2005, Bernoulli 11, 359–379), robustness to nonsynchronous data is obtained. The proposed estimators are shown to have good finite sample performances in Monte Carlo simulations even with an observation frequency low enough to make microstructure noises’ impact on data negligible.