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

Statistical inference in factor analysis for diffusion processes from discrete observations