Quasi-Bayesian information criterion of SEM for diffusion processes based on high-frequency data

We deal with a model selection problem for structural equation modeling (SEM) for diffusion processes. Based on the asymptotic expansion of the marginal quasi-log likelihood, we propose two types of quasi-Bayesian information criteria of the SEM. It is shown that the information criteria have model selection consistency. Furthermore, we examine the finite-sample performance of the proposed information criteria by numerical experiments.