Statistical inference in factor analysis for diffusion processes from discrete observations

TL;DR

This paper develops a new statistical inference method for factor analysis in diffusion processes from discrete data, addressing limitations of existing PCA and quasi-likelihood approaches especially when factors are latent and dimensions are moderate.

Contribution

The paper introduces a novel inference method suitable for latent factors in diffusion processes, overcoming the restrictions of PCA and quasi-likelihood methods.

Findings

Effective for latent factors in diffusion processes

Applicable to moderate-dimensional data

Outperforms existing PCA-based methods

Abstract

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.