Predictive information criterion for jump diffusion processes

In this paper, we address a model selection problem for ergodic jump diffusion processes based on high-frequency samples. We evaluate the expected genuine log-likelihood function and derive an Akaike-type information criterion based on the threshold-based quasi-likelihood function. In the derivation process, we also give new estimates of the transition density of jump diffusion processes. We also provide the relative selection probability of the proposed information criterion.