# Statistical inference for misspecified ergodic L\'evy driven stochastic differential equation models

## TL;DR

This paper demonstrates that Gaussian quasi-likelihood estimators for misspecified ergodic Lévy-driven SDEs are reliable, achieving asymptotic normality and tail probability bounds, thus confirming their practical effectiveness.

## Contribution

It extends the Gaussian quasi-likelihood approach to misspecified ergodic Lévy-driven SDE models, providing theoretical guarantees under misspecification.

## Key findings

- Estimators satisfy tail probability estimates.
- Estimators achieve asymptotic normality.
- Method remains effective under model misspecification.

## Abstract

This paper deals with the estimation problem of misspecified ergodic L\'evy driven stochastic differential equation models based on high-frequency samples. We utilize the widely applicable and tractable Gaussian quasi-likelihood approach which focuses on (conditional) mean and variance structure. It is shown that the corresponding Gaussian quasi-likelihood estimators of drift and scale parameters satisfy tail probability estimates and asymptotic normality at the same rate as correctly specified case. In this process, extended Poisson equation for time-homogeneous Feller Markov processes plays an important role to handle misspecification effect. Our result confirms the practical usefulness of the Gaussian quasi-likelihood approach for SDE models, more firmly.