Statistical inference in SEM for diffusion processes with jumps based on high-frequency data

TL;DR

This paper develops statistical methods for parameter estimation and model testing in SEM for jump diffusion processes using high-frequency data, establishing theoretical properties and validating with simulations.

Contribution

It introduces a quasi-likelihood approach for SEM with jumps, proving consistency, asymptotic normality, and constructing likelihood ratio tests for model validation.

Findings

Quasi-maximum likelihood estimator is consistent and asymptotically normal.

Likelihood ratio test statistics are asymptotically valid.

Numerical simulations support theoretical results.

Abstract

We study structural equation modeling (SEM) for diffusion processes with jumps. Based on high-frequency data, we consider the parameter estimation and the goodness-of-fit test in the SEM. Using a threshold method, we propose the quasi-likelihood of the SEM and prove that the quasi-maximum likelihood estimator has consistency and asymptotic normality. To examine whether a specified parametric model is correct or not, we also construct the quasi-likelihood ratio test statistics and investigate the asymptotic properties. Furthermore, numerical simulations are conducted.