Statistical inference in factor analysis for diffusion processes from discrete observations

We consider statistical inference in factor analysis for ergodic and non-ergodic diffusion processes from discrete observations. Factor model based on high frequency time series data has been mainly discussed in the field of high dimensional covariance matrix estimation. In this field, the method based on principal component analysis has been mainly used. However, this method is effective only for high dimensional model. On the other hand, there is a method based on the quasi-likelihood. However, since the factor is assumed to be observable, we cannot use this method when the factor is latent. Thus, the existing methods are not effective when the factor is latent and the dimension of the observable variable is not so high. Therefore, we propose an effective method in the situation.