  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.
