Accurate prediction of high-dimensional covariance matrices is crucial for portfolio and risk management. In the model developed in this work, high-frequency financial data is used to obtain the realized covariance matrix, and the realized semicovariance is used to decompose the covariance...

We establish a feasible central limit theorem with convergence rate $n^{1/8}$ for the estimation of the {integrated volatility of volatility} (VoV) based on noisy high-frequency data with jumps. This is the first inference theory ever built for VoV estimation under such a general setup. The...