  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.
