Statistical inference for misspecified ergodic Levy driven stochastic differential equation models

We consider the estimation problem of misspecified ergodic Levy driven stochastic differential equation models based on high-frequency samples. We utilize a widely applicable and tractable Gaussian quasi likelihood approach which focuses on mean and variance structure. It is shown that the Gaussian quasi likelihood estimators of the drift and scale parameters still satisfy polynomial type probability estimates and asymptotic normality at the same rate as the correctly specified case. In their derivation process, the theory of extended Poisson equation for time-homogeneous Feller Markov processes plays an important role. Our result confirms the reliability of the Gaussian quasi-likelihood approach for SDE models. (C) 2018 Elsevier B.V. All rights reserved.