We consider a model selection problem for structural equation modeling (SEM) with latent variables for diffusion processes based on high-frequency data. First, we propose the quasi-Akaike information criterion of the SEM and study the asymptotic properties. Next, we consider the situation where the set of competing models includes some misspecified parametric models. It is shown that the probability of choosing the misspecified models converges to zero. Furthermore, examples and simulation results are given.

翻译：本文考虑基于高频数据的扩散过程中带潜变量的结构方程模型（SEM）模型选择问题。首先，我们提出结构方程模型的准赤池信息准则并研究其渐近性质。其次，考虑竞争模型集合包含若干错误设定参数模型的情形。研究表明，选择错误设定模型的概率收敛于零。最后，给出实例及模拟结果。