Testing for non-correlation between price and volatility jumps

We consider a log-price process X_t, which is observed at discrete times 0,Δ_n, 2Δ_n,…, and the process has a stochastic squared volatility σ_t². Assuming that the price process as well as the volatility process have common jumps, we suggest tests for non-correlation between log-price and squared volatility jumps, or functions of such jumps. Our tests have a prescribed asymptotic level, as the mesh Δ_n tends to 0 and the observation time T_n tends to ∞. The finite sample performance of our test is studied using simulations. We finally apply our tests to real data, and the test rejects the non-correlation hypothesis for the combination of squared log-price jumps and the moduli of the jumps of the squared volatility. This sheds new light on economically motivated statements on causality between price and volatility jumps and on econometric modeling.