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 data and is robust to market microstructure frictions. For the test, local estimators of volatility jumps at price jump arrival times are designed using a nonparametric spectral estimator of the spot volatility process. A simulation study and an empirical example with NASDAQ order book data demonstrate the practicability of the proposed methods and highlight the important role played by price volatility co-jumps.
"Common price and volatility jumps in noisy high-frequency data." Electron. J. Statist. 12 (1) 2018 - 2073, 2018. https://doi.org/10.1214/18-EJS1444