Robust covariance estimation with noisy high-frequency financial data

We propose consistent and efficient robust different time-scales estimators to mitigate the heavy-tail effect of high-frequency financial data. Our estimators are based on minimising the Huber loss function with a suitable threshold. We show these estimators are guaranteed to be robust to measurement noise of certain types and jumps. With only finite fourth moments of the observation log-price data, we develop the sub-Gaussian concentration of our estimators around the volatility. We conduct the simulation studies to show the finite sample performance of the proposed estimation methods. The simulation studies imply that our methods are also robust to financial data in the presence of jumps. Empirical studies demonstrate the practical relevance and advantages of our estimators.