We introduce a statistical test for simultaneous jumps in the price of a financial asset and its volatility process. The proposed test is based on high-frequency tick-data and is robust to market microstructure frictions. To localize volatility jumps, we design and analyze a nonparametric...

We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance...

This work develops change-point methods for statistics of high-frequency data. The main interest is the volatility of an Itô semi-martingale, which is discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate different smoothness classes of the...