Gaussian quasi-information criteria for ergodic Lévy driven SDE

We consider relative model comparison for the parametric coefficients of an ergodic Lévy driven observed at high-frequency. Our asymptotics is based on fully explicit two-stage Gaussian quasi-likelihood function (GQLF) Euler-approximation type. For selections scale and drift coefficients, we propose quasi-AIC quasi-BIC statistics through stepwise inference procedure, prove their asymptotic properties. In particular, show that mixed-rates structure joint GQLF, which does not emerge in case diffusions, gives rise to non-standard forms regularization terms selection coefficient, quantitatively clarifying relation between estimation precision sampling frequency. Also shown strategies are essential both tractable derivation properties quasi-information criteria. Numerical experiments given illustrate our theoretical findings.