Detecting jumps in stochastic volatility jump-diffusion models via the power variation approach

It is well-known that pretesting the presence of the jump component in an underlying price process is crucial for modeling this process. In this paper, we propose a consistent test for jump intensity of the conditional Poisson process in a stochastic volatility jump diffusion model. Theoretically, we derive the infill and long-span asymptotic properties of realized power variation under some suitable conditions, and verify the asymptotic size and power of the proposed test. Furthermore, the finite-sample performance of our proposed test is illustrated through simulation analysis, and an application to real price series provides empirical evidence of significant jump intensities.