Structural equation modeling with latent variables for diffusion processes based on high-frequency data

TL;DR

This paper develops a structural equation modeling framework with latent variables for diffusion processes using high-frequency data, introducing quasi-likelihood estimators and goodness-of-fit tests with proven asymptotic properties.

Contribution

It introduces a novel SEM approach for diffusion processes with high-frequency data, including new estimators and goodness-of-fit tests with theoretical validation.

Findings

Consistent quasi-likelihood estimators derived

Goodness-of-fit test based on likelihood ratio proposed

Asymptotic properties of estimators established

Abstract

We consider structural equation modeling (SEM) with latent variables for diffusion processes based on high-frequency data. We derive the quasi-likelihood estimators for parameters in the SEM. The goodness-of-fit test based on the quasi-likelihood ratio is proposed. Furthermore, the asymptotic properties of our proposed estimators are examined.